⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
[[File:pendulum.gif|160px|thumb|right|Capture of the Oz version.]]
{{task|Temporal media}}{{requires|Graphics}} One good way of making an animation is by simulating a physical system and illustrating the variables in that system using a dynamically changing graphical display. The classic such physical system is a [[wp:Pendulum|simple gravity pendulum]].
For this task, create a simple physical model of a pendulum and animate it.
Ada
This does not use a GUI, it simply animates the pendulum and prints out the positions. If you want, you can replace the output method with graphical update methods.
X and Y are relative positions of the pendulum to the anchor.
pendulums.ads:
generic
type Float_Type is digits <>;
Gravitation : Float_Type;
package Pendulums is
type Pendulum is private;
function New_Pendulum (Length : Float_Type;
Theta0 : Float_Type) return Pendulum;
function Get_X (From : Pendulum) return Float_Type;
function Get_Y (From : Pendulum) return Float_Type;
procedure Update_Pendulum (Item : in out Pendulum; Time : in Duration);
private
type Pendulum is record
Length : Float_Type;
Theta : Float_Type;
X : Float_Type;
Y : Float_Type;
Velocity : Float_Type;
end record;
end Pendulums;
pendulums.adb:
with Ada.Numerics.Generic_Elementary_Functions;
package body Pendulums is
package Math is new Ada.Numerics.Generic_Elementary_Functions (Float_Type);
function New_Pendulum (Length : Float_Type;
Theta0 : Float_Type) return Pendulum is
Result : Pendulum;
begin
Result.Length := Length;
Result.Theta := Theta0 / 180.0 * Ada.Numerics.Pi;
Result.X := Math.Sin (Theta0) * Length;
Result.Y := Math.Cos (Theta0) * Length;
Result.Velocity := 0.0;
return Result;
end New_Pendulum;
function Get_X (From : Pendulum) return Float_Type is
begin
return From.X;
end Get_X;
function Get_Y (From : Pendulum) return Float_Type is
begin
return From.Y;
end Get_Y;
procedure Update_Pendulum (Item : in out Pendulum; Time : in Duration) is
Acceleration : constant Float_Type := Gravitation / Item.Length *
Math.Sin (Item.Theta);
begin
Item.X := Math.Sin (Item.Theta) * Item.Length;
Item.Y := Math.Cos (Item.Theta) * Item.Length;
Item.Velocity := Item.Velocity +
Acceleration * Float_Type (Time);
Item.Theta := Item.Theta +
Item.Velocity * Float_Type (Time);
end Update_Pendulum;
end Pendulums;
example main.adb:
with Ada.Text_IO;
with Ada.Calendar;
with Pendulums;
procedure Main is
package Float_Pendulum is new Pendulums (Float, -9.81);
use Float_Pendulum;
use type Ada.Calendar.Time;
My_Pendulum : Pendulum := New_Pendulum (10.0, 30.0);
Now, Before : Ada.Calendar.Time;
begin
Before := Ada.Calendar.Clock;
loop
Delay 0.1;
Now := Ada.Calendar.Clock;
Update_Pendulum (My_Pendulum, Now - Before);
Before := Now;
-- output positions relative to origin
-- replace with graphical output if wanted
Ada.Text_IO.Put_Line (" X: " & Float'Image (Get_X (My_Pendulum)) &
" Y: " & Float'Image (Get_Y (My_Pendulum)));
end loop;
end Main;
{{out}}
X: 5.00000E+00 Y: 8.66025E+00
X: 4.95729E+00 Y: 8.68477E+00
X: 4.87194E+00 Y: 8.73294E+00
X: 4.74396E+00 Y: 8.80312E+00
X: 4.57352E+00 Y: 8.89286E+00
X: 4.36058E+00 Y: 8.99919E+00
X: 4.10657E+00 Y: 9.11790E+00
X: 3.81188E+00 Y: 9.24498E+00
X: 3.47819E+00 Y: 9.37562E+00
X: 3.10714E+00 Y: 9.50504E+00
X: 2.70211E+00 Y: 9.62801E+00
X: 2.26635E+00 Y: 9.73980E+00
X: 1.80411E+00 Y: 9.83591E+00
X: 1.32020E+00 Y: 9.91247E+00
X: 8.20224E-01 Y: 9.96630E+00
X: 3.10107E-01 Y: 9.99519E+00
X: -2.03865E-01 Y: 9.99792E+00
X: -7.15348E-01 Y: 9.97438E+00
X: -1.21816E+00 Y: 9.92553E+00
X: -1.70581E+00 Y: 9.85344E+00
X: -2.17295E+00 Y: 9.76106E+00
X: -2.61452E+00 Y: 9.65216E+00
X: -3.02618E+00 Y: 9.53112E+00
X: -3.40427E+00 Y: 9.40271E+00
X: -3.74591E+00 Y: 9.27190E+00
X: -4.04873E+00 Y: 9.14373E+00
X: -4.31141E+00 Y: 9.02285E+00
X: -4.53271E+00 Y: 8.91373E+00
X: -4.71186E+00 Y: 8.82034E+00
X: -4.84868E+00 Y: 8.74587E+00
X: -4.94297E+00 Y: 8.69293E+00
X: -4.99459E+00 Y: 8.66337E+00
X: -5.00352E+00 Y: 8.65822E+00
...
AutoHotkey
This version doesn't use an complex physics calculation - I found a faster way. {{libheader|GDIP}}
SetBatchlines,-1
;settings
SizeGUI:={w:650,h:400} ;Guisize
pendulum:={length:300,maxangle:90,speed:2,size:30,center:{x:Sizegui.w//2,y:10}} ;pendulum length, size, center, speed and maxangle
pendulum.maxangle:=pendulum.maxangle*0.01745329252
p_Token:=Gdip_Startup()
Gui,+LastFound
Gui,show,% "w" SizeGUI.w " h" SizeGUI.h
hwnd:=WinActive()
hdc:=GetDC(hwnd)
start:=A_TickCount/1000
G:=Gdip_GraphicsFromHDC(hdc)
pBitmap:=Gdip_CreateBitmap(650, 450)
G2:=Gdip_GraphicsFromImage(pBitmap)
Gdip_SetSmoothingMode(G2, 4)
pBrush := Gdip_BrushCreateSolid(0xff0000FF)
pBrush2 := Gdip_BrushCreateSolid(0xFF777700)
pPen:=Gdip_CreatePenFromBrush(pBrush2, 10)
SetTimer,Update,10
Update:
Gdip_GraphicsClear(G2,0xFFFFFFFF)
time:=start-(A_TickCount/1000*pendulum.speed)
angle:=sin(time)*pendulum.maxangle
x2:=sin(angle)*pendulum.length+pendulum.center.x
y2:=cos(angle)*pendulum.length+pendulum.center.y
Gdip_DrawLine(G2,pPen,pendulum.center.x,pendulum.center.y,x2,y2)
GDIP_DrawCircle(G2,pBrush,pendulum.center.x,pendulum.center.y,15)
GDIP_DrawCircle(G2,pBrush2,x2,y2,pendulum.size)
Gdip_DrawImage(G, pBitmap)
return
GDIP_DrawCircle(g,b,x,y,r){
Gdip_FillEllipse(g, b, x-r//2,y-r//2 , r, r)
}
GuiClose:
ExitApp
BASIC
=
BBC BASIC
= {{works with|BBC BASIC for Windows}}
MODE 8
*FLOAT 64
VDU 23,23,4;0;0;0; : REM Set line thickness
theta = RAD(40) : REM initial displacement
g = 9.81 : REM acceleration due to gravity
l = 0.50 : REM length of pendulum in metres
REPEAT
PROCpendulum(theta, l)
WAIT 1
PROCpendulum(theta, l)
accel = - g * SIN(theta) / l / 100
speed += accel / 100
theta += speed
UNTIL FALSE
END
DEF PROCpendulum(a, l)
LOCAL pivotX, pivotY, bobX, bobY
pivotX = 640
pivotY = 800
bobX = pivotX + l * 1000 * SIN(a)
bobY = pivotY - l * 1000 * COS(a)
GCOL 3,6
LINE pivotX, pivotY, bobX, bobY
GCOL 3,11
CIRCLE FILL bobX + 24 * SIN(a), bobY - 24 * COS(a), 24
ENDPROC
=
Commodore BASIC
=
10 GOSUB 1000
20 THETA = π/2
30 G = 9.81
40 L = 0.5
50 SPEED = 0
60 PX = 20
70 PY = 1
80 BX = PX+L*20*SIN(THETA)
90 BY = PY-L*20*COS(THETA)
100 PRINT CHR$(147);
110 FOR X=PX TO BX STEP (BX-PX)/10
120 Y=PY+(X-PX)*(BY-PY)/(BX-PX)
130 PRINT CHR$(19);LEFT$(X$,X);LEFT$(Y$,Y);"."
140 NEXT
150 PRINT CHR$(19);LEFT$(X$,BX);LEFT$(Y$,BY);CHR$(113)
160 ACCEL=G*SIN(THETA)/L/50
170 SPEED=SPEED+ACCEL/10
180 THETA=THETA+SPEED
190 GOTO 80
980 REM ** SETUP STRINGS TO BE USED **
990 REM ** FOR CURSOR POSITIONING **
1000 FOR I=0 TO 39: X$ = X$+CHR$(29): NEXT
1010 FOR I=0 TO 24: Y$ = Y$+CHR$(17): NEXT
1020 RETURN
=
FreeBASIC
=
Const PI = 3.141592920
Dim As Double theta, g, l, accel, speed, px, py, bx, by
theta = PI/2
g = 9.81
l = 1
speed = 0
px = 320
py = 10
Screen 17 '640x400 graphic
Do
bx=px+l*300*Sin(theta)
by=py-l*300*Cos(theta)
Cls
Line (px,py)-(bx,by)
Circle (bx,by),5,,,,,F
accel=g*Sin(theta)/l/100
speed=speed+accel/100
theta=theta+speed
Draw String (0,370), "Pendulum"
Draw String (0,385), "Press any key to quit"
Sleep 10
Loop Until Inkey()<>""
==={{header|IS-BASIC}}===
## C
{{libheader|GLUT}}
```cpp
#include <iostream>
#include <math.h>
#include <GL/glut.h>
#include <GL/gl.h>
#include <sys/time.h>
#define length 5
#define g 9.8
double alpha, accl, omega = 0, E;
struct timeval tv;
double elappsed() {
struct timeval now;
gettimeofday(&now, 0);
int ret = (now.tv_sec - tv.tv_sec) * 1000000
+ now.tv_usec - tv.tv_usec;
tv = now;
return ret / 1.e6;
}
void resize(int w, int h)
{
glViewport(0, 0, w, h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glOrtho(0, w, h, 0, -1, 1);
}
void render()
{
double x = 320 + 300 * sin(alpha), y = 300 * cos(alpha);
resize(640, 320);
glClear(GL_COLOR_BUFFER_BIT);
glBegin(GL_LINES);
glVertex2d(320, 0);
glVertex2d(x, y);
glEnd();
glFlush();
double us = elappsed();
alpha += (omega + us * accl / 2) * us;
omega += accl * us;
/* don't let precision error go out of hand */
if (length * g * (1 - cos(alpha)) >= E) {
alpha = (alpha < 0 ? -1 : 1) * acos(1 - E / length / g);
omega = 0;
}
accl = -g / length * sin(alpha);
}
void init_gfx(int *c, char **v)
{
glutInit(c, v);
glutInitDisplayMode(GLUT_RGB);
glutInitWindowSize(640, 320);
glutIdleFunc(render);
glutCreateWindow("Pendulum");
}
int main(int c, char **v)
{
alpha = 4 * atan2(1, 1) / 2.1;
E = length * g * (1 - cos(alpha));
accl = -g / length * sin(alpha);
omega = 0;
gettimeofday(&tv, 0);
init_gfx(&c, v);
glutMainLoop();
return 0;
}
C++
{{libheader|wxWidgets}} File wxPendulumDlg.hpp
#ifndef __wxPendulumDlg_h__ #define __wxPendulumDlg_h__ // --------------------- /// @author Martin Ettl /// @date 2013-02-03 // --------------------- #ifdef __BORLANDC__ #pragma hdrstop #endif #ifndef WX_PRECOMP #include <wx/wx.h> #include <wx/dialog.h> #else #include <wx/wxprec.h> #endif #include <wx/timer.h> #include <wx/dcbuffer.h> #include <cmath> class wxPendulumDlgApp : public wxApp { public: bool OnInit(); int OnExit(); }; class wxPendulumDlg : public wxDialog { public: wxPendulumDlg(wxWindow *parent, wxWindowID id = 1, const wxString &title = wxT("wxPendulum"), const wxPoint& pos = wxDefaultPosition, const wxSize& size = wxDefaultSize, long style = wxSUNKEN_BORDER | wxCAPTION | wxRESIZE_BORDER | wxSYSTEM_MENU | wxDIALOG_NO_PARENT | wxMINIMIZE_BOX | wxMAXIMIZE_BOX | wxCLOSE_BOX); virtual ~wxPendulumDlg(); // Event handler void wxPendulumDlgPaint(wxPaintEvent& event); void wxPendulumDlgSize(wxSizeEvent& event); void OnTimer(wxTimerEvent& event); private: // a pointer to a timer object wxTimer *m_timer; unsigned int m_uiLength; double m_Angle; double m_AngleVelocity; enum wxIDs { ID_WXTIMER1 = 1001, ID_DUMMY_VALUE_ }; void OnClose(wxCloseEvent& event); void CreateGUIControls(); DECLARE_EVENT_TABLE() }; #endif // __wxPendulumDlg_h__
File wxPendulumDlg.cpp
// --------------------- /// @author Martin Ettl /// @date 2013-02-03 // --------------------- #include "wxPendulumDlg.hpp" #include <wx/pen.h> IMPLEMENT_APP(wxPendulumDlgApp) bool wxPendulumDlgApp::OnInit() { wxPendulumDlg* dialog = new wxPendulumDlg(NULL); SetTopWindow(dialog); dialog->Show(true); return true; } int wxPendulumDlgApp::OnExit() { return 0; } BEGIN_EVENT_TABLE(wxPendulumDlg, wxDialog) EVT_CLOSE(wxPendulumDlg::OnClose) EVT_SIZE(wxPendulumDlg::wxPendulumDlgSize) EVT_PAINT(wxPendulumDlg::wxPendulumDlgPaint) EVT_TIMER(ID_WXTIMER1, wxPendulumDlg::OnTimer) END_EVENT_TABLE() wxPendulumDlg::wxPendulumDlg(wxWindow *parent, wxWindowID id, const wxString &title, const wxPoint &position, const wxSize& size, long style) : wxDialog(parent, id, title, position, size, style) { CreateGUIControls(); } wxPendulumDlg::~wxPendulumDlg() { } void wxPendulumDlg::CreateGUIControls() { SetIcon(wxNullIcon); SetSize(8, 8, 509, 412); Center(); m_uiLength = 200; m_Angle = M_PI/2.; m_AngleVelocity = 0; m_timer = new wxTimer(); m_timer->SetOwner(this, ID_WXTIMER1); m_timer->Start(20); } void wxPendulumDlg::OnClose(wxCloseEvent& WXUNUSED(event)) { Destroy(); } void wxPendulumDlg::wxPendulumDlgPaint(wxPaintEvent& WXUNUSED(event)) { SetBackgroundStyle(wxBG_STYLE_CUSTOM); wxBufferedPaintDC dc(this); // Get window dimensions wxSize sz = GetClientSize(); // determine the center of the canvas const wxPoint center(wxPoint(sz.x / 2, sz.y / 2)); // create background color wxColour powderblue = wxColour(176,224,230); // draw powderblue background dc.SetPen(powderblue); dc.SetBrush(powderblue); dc.DrawRectangle(0, 0, sz.x, sz.y); // draw lines wxPen Pen(*wxBLACK_PEN); Pen.SetWidth(1); dc.SetPen(Pen); dc.SetBrush(*wxBLACK_BRUSH); double angleAccel, dt = 0.15; angleAccel = (-9.81 / m_uiLength) * sin(m_Angle); m_AngleVelocity += angleAccel * dt; m_Angle += m_AngleVelocity * dt; int anchorX = sz.x / 2, anchorY = sz.y / 4; int ballX = anchorX + (int)(sin(m_Angle) * m_uiLength); int ballY = anchorY + (int)(cos(m_Angle) * m_uiLength); dc.DrawLine(anchorX, anchorY, ballX, ballY); dc.SetBrush(*wxGREY_BRUSH); dc.DrawEllipse(anchorX - 3, anchorY - 4, 7, 7); dc.SetBrush(wxColour(255,255,0)); // yellow dc.DrawEllipse(ballX - 7, ballY - 7, 20, 20); } void wxPendulumDlg::wxPendulumDlgSize(wxSizeEvent& WXUNUSED(event)) { Refresh(); } void wxPendulumDlg::OnTimer(wxTimerEvent& WXUNUSED(event)) { // force refresh Refresh(); }
This program is tested with wxWidgets version 2.8 and 2.9. The whole project, including makefile for compiling on Linux can be download from [https://github.com/orbitcowboy/wxPendulum github]. [[File:WxPendulumScreenshot.png]]
C#
{{libheader|Windows Forms}}
{{libheader|GDI (System.Drawing)}}
using System; using System.Drawing; using System.Windows.Forms; class CSharpPendulum { Form _form; Timer _timer; double _angle = Math.PI / 2, _angleAccel, _angleVelocity = 0, _dt = 0.1; int _length = 50; [STAThread] static void Main() { var p = new CSharpPendulum(); } public CSharpPendulum() { _form = new Form() { Text = "Pendulum", Width = 200, Height = 200 }; _timer = new Timer() { Interval = 30 }; _timer.Tick += delegate(object sender, EventArgs e) { int anchorX = (_form.Width / 2) - 12, anchorY = _form.Height / 4, ballX = anchorX + (int)(Math.Sin(_angle) * _length), ballY = anchorY + (int)(Math.Cos(_angle) * _length); _angleAccel = -9.81 / _length * Math.Sin(_angle); _angleVelocity += _angleAccel * _dt; _angle += _angleVelocity * _dt; Bitmap dblBuffer = new Bitmap(_form.Width, _form.Height); Graphics g = Graphics.FromImage(dblBuffer); Graphics f = Graphics.FromHwnd(_form.Handle); g.DrawLine(Pens.Black, new Point(anchorX, anchorY), new Point(ballX, ballY)); g.FillEllipse(Brushes.Black, anchorX - 3, anchorY - 4, 7, 7); g.FillEllipse(Brushes.DarkGoldenrod, ballX - 7, ballY - 7, 14, 14); f.Clear(Color.White); f.DrawImage(dblBuffer, new Point(0, 0)); }; _timer.Start(); Application.Run(_form); } }
Clojure
Clojure solution using an atom and a separate rendering thread
{{libheader|Swing}} {{libheader|AWT}}
(ns pendulum (:import (javax.swing JFrame) (java.awt Canvas Graphics Color))) (def length 200) (def width (* 2 (+ 50 length))) (def height (* 3 (/ length 2))) (def dt 0.1) (def g 9.812) (def k (- (/ g length))) (def anchor-x (/ width 2)) (def anchor-y (/ height 8)) (def angle (atom (/ (Math/PI) 2))) (defn draw [#^Canvas canvas angle] (let [buffer (.getBufferStrategy canvas) g (.getDrawGraphics buffer) ball-x (+ anchor-x (* (Math/sin angle) length)) ball-y (+ anchor-y (* (Math/cos angle) length))] (try (doto g (.setColor Color/BLACK) (.fillRect 0 0 width height) (.setColor Color/RED) (.drawLine anchor-x anchor-y ball-x ball-y) (.setColor Color/YELLOW) (.fillOval (- anchor-x 3) (- anchor-y 4) 7 7) (.fillOval (- ball-x 7) (- ball-y 7) 14 14)) (finally (.dispose g))) (if-not (.contentsLost buffer) (.show buffer)) )) (defn start-renderer [canvas] (->> (fn [] (draw canvas @angle) (recur)) (new Thread) (.start))) (defn -main [& args] (let [frame (JFrame. "Pendulum") canvas (Canvas.)] (doto frame (.setSize width height) (.setDefaultCloseOperation JFrame/EXIT_ON_CLOSE) (.setResizable false) (.add canvas) (.setVisible true)) (doto canvas (.createBufferStrategy 2) (.setVisible true) (.requestFocus)) (start-renderer canvas) (loop [v 0] (swap! angle #(+ % (* v dt))) (Thread/sleep 15) (recur (+ v (* k (Math/sin @angle) dt)))) )) (-main)
Common Lisp
An approach using closures. Physics code adapted from [[Animate_a_pendulum#Ada|Ada]].
{{libheader|Lispbuilder-SDL}}
Pressing the spacebar adds a pendulum.
(defvar *frame-rate* 30) (defvar *damping* 0.99 "Deceleration factor.") (defun make-pendulum (length theta0 x) "Returns an anonymous function with enclosed state representing a pendulum." (let* ((theta (* (/ theta0 180) pi)) (acceleration 0)) (if (< length 40) (setf length 40)) ;;avoid a divide-by-zero (lambda () ;;Draws the pendulum, updating its location and speed. (sdl:draw-line (sdl:point :x x :y 1) (sdl:point :x (+ (* (sin theta) length) x) :y (* (cos theta) length))) (sdl:draw-filled-circle (sdl:point :x (+ (* (sin theta) length) x) :y (* (cos theta) length)) 20 :color sdl:*yellow* :stroke-color sdl:*white*) ;;The magic constant approximates the speed we want for a given frame-rate. (incf acceleration (* (sin theta) (* *frame-rate* -0.001))) (incf theta acceleration) (setf acceleration (* acceleration *damping*))))) (defun main (&optional (w 640) (h 480)) (sdl:with-init () (sdl:window w h :title-caption "Pendulums" :fps (make-instance 'sdl:fps-fixed)) (setf (sdl:frame-rate) *frame-rate*) (let ((pendulums nil)) (sdl:with-events () (:quit-event () t) (:idle () (sdl:clear-display sdl:*black*) (mapcar #'funcall pendulums) ;;Draw all the pendulums (sdl:update-display)) (:key-down-event (:key key) (cond ((sdl:key= key :sdl-key-escape) (sdl:push-quit-event)) ((sdl:key= key :sdl-key-space) (push (make-pendulum (random (- h 100)) (random 90) (round w 2)) pendulums))))))))
E
{{works with|E-on-Java}} (Uses Java Swing for GUI. The animation logic is independent, however.)
The angle of a pendulum with length and acceleration due to gravity with all its mass at the end and no friction/air resistance has an acceleration at any given moment of : This simulation uses this formula directly, updating the velocity from the acceleration and the position from the velocity; inaccuracy results from the finite timestep.
The event flow works like this:
The ''clock'' object created by the simulation steps the simulation on the specified in the interval.
The simulation writes its output to angle, which is a ''Lamport slot'' which can notify of updates.
The ''whenever'' set up by makeDisplayComponent listens for updates and triggers redrawing as long as ''interest'' has been expressed, which is done whenever the component actually redraws, which happens only if the component's window is still on screen.
When the window is closed, additionally, the simulation itself is stopped and the application allowed to exit.
(This logic is more general than necessary; it is designed to be suitable for a larger application as well.)
#!/usr/bin/env rune
pragma.syntax("0.9")
def pi := (-1.0).acos()
def makeEPainter := <unsafe:com.zooko.tray.makeEPainter>
def makeLamportSlot := <import:org.erights.e.elib.slot.makeLamportSlot>
def whenever := <import:org.erights.e.elib.slot.whenever>
def colors := <import:java.awt.makeColor>
# --------------------------------------------------------------
# --- Definitions
def makePendulumSim(length_m :float64,
gravity_mps2 :float64,
initialAngle_rad :float64,
timestep_ms :int) {
var velocity := 0
def &angle := makeLamportSlot(initialAngle_rad)
def k := -gravity_mps2/length_m
def timestep_s := timestep_ms / 1000
def clock := timer.every(timestep_ms, fn _ {
def acceleration := k * angle.sin()
velocity += acceleration * timestep_s
angle += velocity * timestep_s
})
return [clock, &angle]
}
def makeDisplayComponent(&angle) {
def c
def updater := whenever([&angle], fn { c.repaint() })
bind c := makeEPainter(def paintCallback {
to paintComponent(g) {
try {
def originX := c.getWidth() // 2
def originY := c.getHeight() // 2
def pendRadius := (originX.min(originY) * 0.95).round()
def ballRadius := (originX.min(originY) * 0.04).round()
def ballX := (originX + angle.sin() * pendRadius).round()
def ballY := (originY + angle.cos() * pendRadius).round()
g.setColor(colors.getWhite())
g.fillRect(0, 0, c.getWidth(), c.getHeight())
g.setColor(colors.getBlack())
g.fillOval(originX - 2, originY - 2, 4, 4)
g.drawLine(originX, originY, ballX, ballY)
g.fillOval(ballX - ballRadius, ballY - ballRadius, ballRadius * 2, ballRadius * 2)
updater[] # provoke interest provided that we did get drawn (window not closed)
} catch p {
stderr.println(`In paint callback: $p${p.eStack()}`)
}
}
})
c.setPreferredSize(<awt:makeDimension>(300, 300))
return c
}
# --------------------------------------------------------------
# --- Application setup
def [clock, &angle] := makePendulumSim(1, 9.80665, pi*99/100, 10)
# Initialize AWT, move to AWT event thread
when (currentVat.morphInto("awt")) -> {
# Create the window
def frame := <unsafe:javax.swing.makeJFrame>("Pendulum")
frame.setContentPane(def display := makeDisplayComponent(&angle))
frame.addWindowListener(def mainWindowListener {
to windowClosing(_) {
clock.stop()
interp.continueAtTop()
}
match _ {}
})
frame.setLocation(50, 50)
frame.pack()
# Start and become visible
frame.show()
clock.start()
}
interp.blockAtTop()
EasyLang
[https://easylang.online/apps/pendulum.html Run it]
## Elm
```elm
import Color exposing (..)
import Collage exposing (..)
import Element exposing (..)
import Html exposing (..)
import Time exposing (..)
import Html.App exposing (program)
dt = 0.01
scale = 100
type alias Model =
{ angle : Float
, angVel : Float
, length : Float
, gravity : Float
}
type Msg
= Tick Time
init : (Model,Cmd Msg)
init =
( { angle = 3 * pi / 4
, angVel = 0.0
, length = 2
, gravity = -9.81
}
, Cmd.none)
update : Msg -> Model -> (Model, Cmd Msg)
update _ model =
let
angAcc = -1.0 * (model.gravity / model.length) * sin (model.angle)
angVel' = model.angVel + angAcc * dt
angle' = model.angle + angVel' * dt
in
( { model
| angle = angle'
, angVel = angVel'
}
, Cmd.none )
view : Model -> Html Msg
view model =
let
endPoint = ( 0, scale * model.length )
pendulum =
group
[ segment ( 0, 0 ) endPoint
|> traced { defaultLine | width = 2, color = red }
, circle 8
|> filled blue
, ngon 3 10
|> filled green
|> rotate (pi/2)
|> move endPoint
]
in
toHtml <|
collage 700 500
[ pendulum |> rotate model.angle ]
subscriptions : Model -> Sub Msg
subscriptions _ =
Time.every (dt * second) Tick
main =
program
{ init = init
, view = view
, update = update
, subscriptions = subscriptions
}
Link to live demo: http://dc25.github.io/animatedPendulumElm
ERRE
PROGRAM PENDULUM
!
! for rosettacode.org
!
!$KEY
!$INCLUDE="PC.LIB"
PROCEDURE PENDULUM(A,L)
PIVOTX=320
PIVOTY=0
BOBX=PIVOTX+L*500*SIN(a)
BOBY=PIVOTY+L*500*COS(a)
LINE(PIVOTX,PIVOTY,BOBX,BOBY,6,FALSE)
CIRCLE(BOBX+24*SIN(A),BOBY+24*COS(A),27,11)
PAUSE(0.01)
LINE(PIVOTX,PIVOTY,BOBX,BOBY,0,FALSE)
CIRCLE(BOBX+24*SIN(A),BOBY+24*COS(A),27,0)
END PROCEDURE
BEGIN
SCREEN(9)
THETA=40*p/180 ! initial displacement
G=9.81 ! acceleration due to gravity
L=0.5 ! length of pendulum in metres
LINE(0,0,639,0,5,FALSE)
LOOP
PENDULUM(THETA,L)
ACCEL=-G*SIN(THETA)/L/100
SPEED=SPEED+ACCEL/100
THETA=THETA+SPEED
END LOOP
END PROGRAM
PC version: Ctrl+Break to stop.
Euphoria
DOS32 version
{{works with|Euphoria|3.1.1}}
include graphics.e
include misc.e
constant dt = 1E-3
constant g = 50
sequence vc
sequence suspension
atom len
procedure draw_pendulum(atom color, atom len, atom alfa)
sequence point
point = (len*{sin(alfa),cos(alfa)} + suspension)
draw_line(color, {suspension, point})
ellipse(color,0,point-{10,10},point+{10,10})
end procedure
function wait()
atom t0
t0 = time()
while time() = t0 do
if get_key() != -1 then
return 1
end if
end while
return 0
end function
procedure animation()
atom alfa, omega, epsilon
if graphics_mode(18) then
end if
vc = video_config()
suspension = {vc[VC_XPIXELS]/2,vc[VC_YPIXELS]/2}
len = vc[VC_YPIXELS]/2-20
alfa = PI/2
omega = 0
while 1 do
draw_pendulum(BRIGHT_WHITE,len,alfa)
if wait() then
exit
end if
draw_pendulum(BLACK,len,alfa)
epsilon = -len*sin(alfa)*g
omega += dt*epsilon
alfa += dt*omega
end while
if graphics_mode(-1) then
end if
end procedure
animation()
Euler Math Toolbox
Euler Math Toolbox can determine the exact period of a physical pendulum. The result is then used to animate the pendulum. The following code is ready to be pasted back into Euler notebooks.
>g=gearth$; l=1m;
>function f(x,y) := [y[2],-g*sin(y[1])/l]
>function h(a) := ode("f",linspace(0,a,100),[0,2])[1,-1]
>period=solve("h",2)
2.06071780729
>t=linspace(0,period,30); s=ode("f",t,[0,2])[1];
>function anim (t,s) ...
$ setplot(-1,1,-1,1);
$ markerstyle("o#");
$ repeat
$ for i=1 to cols(t)-1;
$ clg;
$ hold on;
$ plot([0,sin(s[i])],[1,1-cos(s[i])]);
$ mark([0,sin(s[i])],[1,1-cos(s[i])]);
$ hold off;
$ wait(t[i+1]-t[i]);
$ end;
$ until testkey();
$ end
$endfunction
>anim(t,s);
>
FBSL
FBSLSETTEXT(ME, "Pendulum")
FBSL.SETTIMER(ME, 1000, 10)
RESIZE(ME, 0, 0, 300, 200)
CENTER(ME)
SHOW(ME)
BEGIN EVENTS
SELECT CASE CBMSG
CASE WM_TIMER
' Request redraw
InvalidateRect(ME, NULL, FALSE)
RETURN 0
CASE WM_PAINT
Swing()
CASE WM_CLOSE
FBSL.KILLTIMER(ME, 1000)
END SELECT
END EVENTS
SUB Swing()
TYPE RECT: %rcLeft, %rcTop, %rcRight, %rcBottom: END TYPE
STATIC rc AS RECT, !!acceleration, !!velocity, !!angle = M_PI_2, %pendulum = 100
GetClientRect(ME, @rc)
' Recalculate
DIM headX = rc.rcRight / 2, headY = rc.rcBottom / 4
DIM tailX = headX + SIN(angle) * pendulum
DIM tailY = headY + COS(angle) * pendulum
acceleration = -9.81 / pendulum * SIN(angle)
INCR(velocity, acceleration * 0.1)(angle, velocity * 0.1)
' Create backbuffer
CreateCompatibleDC(GetDC(ME))
SelectObject(CreateCompatibleDC, CreateCompatibleBitmap(GetDC, rc.rcRight, rc.rcBottom))
' Draw to backbuffer
FILLSTYLE(FILL_SOLID): FILLCOLOR(RGB(200, 200, 0))
LINE(CreateCompatibleDC, 0, 0, rc.rcRight, rc.rcBottom, GetSysColor(COLOR_BTNHILIGHT), TRUE, TRUE)
LINE(CreateCompatibleDC, 0, headY, rc.rcRight, headY, GetSysColor(COLOR_3DSHADOW))
DRAWWIDTH(3)
LINE(CreateCompatibleDC, headX, headY, tailX, tailY, RGB(200, 0, 0))
DRAWWIDTH(1)
CIRCLE(CreateCompatibleDC, headX, headY, 2, GetSysColor, 0, 360, 1, TRUE)
CIRCLE(CreateCompatibleDC, tailX, tailY, 10, GetSysColor, 0, 360, 1, FALSE)
' Blit to window
BitBlt(GetDC, 0, 0, rc.rcRight, rc.rcBottom, CreateCompatibleDC, 0, 0, SRCCOPY)
ReleaseDC(ME, GetDC)
' Delete backbuffer
DeleteObject(SelectObject(CreateCompatibleDC, SelectObject))
DeleteDC(CreateCompatibleDC)
END SUB
'''Screenshot:''' [[File:FBSLPendulum.png]]
Factor
Approximation of the pendulum for small swings : theta = theta0 * cos(omega0 * t)
USING: accessors alarms arrays calendar colors.constants kernel
locals math math.constants math.functions math.rectangles
math.vectors opengl sequences system ui ui.gadgets ui.render ;
IN: pendulum
CONSTANT: g 9.81
CONSTANT: l 20
CONSTANT: theta0 0.5
: current-time ( -- time ) nano-count -9 10^ * ;
: T0 ( -- T0 ) 2 pi l g / sqrt * * ;
: omega0 ( -- omega0 ) 2 pi * T0 / ;
: theta ( -- theta ) current-time omega0 * cos theta0 * ;
: relative-xy ( theta l -- xy )
swap [ sin * ] [ cos * ] 2bi 2array ;
: theta-to-xy ( origin theta l -- xy ) relative-xy v+ ;
TUPLE: pendulum-gadget < gadget alarm ;
: O ( gadget -- origin ) rect-bounds [ drop ] [ first 2 / ] bi* 0 2array ;
: window-l ( gadget -- l ) rect-bounds [ drop ] [ second ] bi* ;
: gadget-xy ( gadget -- xy ) [ O ] [ drop theta ] [ window-l ] tri theta-to-xy ;
M: pendulum-gadget draw-gadget*
COLOR: black gl-color
[ O ] [ gadget-xy ] bi gl-line ;
M:: pendulum-gadget graft* ( gadget -- )
[ gadget relayout-1 ]
20 milliseconds every gadget (>>alarm) ;
M: pendulum-gadget ungraft* alarm>> cancel-alarm ;
: <pendulum-gadget> ( -- gadget )
pendulum-gadget new
{ 500 500 } >>pref-dim ;
: pendulum-main ( -- )
[ <pendulum-gadget> "pendulum" open-window ] with-ui ;
MAIN: pendulum-main
Fortran
Uses system commands (gfortran) to clear the screen. An initial starting angle is allowed between 90 (to the right) and -90 degrees (to the left). It checks for incorrect inputs.
!Implemented by Anant Dixit (October, 2014)
program animated_pendulum
implicit none
double precision, parameter :: pi = 4.0D0*atan(1.0D0), l = 1.0D-1, dt = 1.0D-2, g = 9.8D0
integer :: io
double precision :: s_ang, c_ang, p_ang, n_ang
write(*,*) 'Enter starting angle (in degrees):'
do
read(*,*,iostat=io) s_ang
if(io.ne.0 .or. s_ang.lt.-90.0D0 .or. s_ang.gt.90.0D0) then
write(*,*) 'Please enter an angle between 90 and -90 degrees:'
else
exit
end if
end do
call execute_command_line('cls')
c_ang = s_ang*pi/180.0D0
p_ang = c_ang
call display(c_ang)
do
call next_time_step(c_ang,p_ang,g,l,dt,n_ang)
if(abs(c_ang-p_ang).ge.0.05D0) then
call execute_command_line('cls')
call display(c_ang)
end if
end do
end program
subroutine next_time_step(c_ang,p_ang,g,l,dt,n_ang)
double precision :: c_ang, p_ang, g, l, dt, n_ang
n_ang = (-g*sin(c_ang)/l)*2.0D0*dt**2 + 2.0D0*c_ang - p_ang
p_ang = c_ang
c_ang = n_ang
end subroutine
subroutine display(c_ang)
double precision :: c_ang
character (len=*), parameter :: cfmt = '(A1)'
double precision :: rx, ry
integer :: x, y, i, j
rx = 45.0D0*sin(c_ang)
ry = 22.5D0*cos(c_ang)
x = int(rx)+51
y = int(ry)+2
do i = 1,32
do j = 1,100
if(i.eq.y .and. j.eq.x) then
write(*,cfmt,advance='no') 'O'
else if(i.eq.y .and. (j.eq.(x-1).or.j.eq.(x+1))) then
write(*,cfmt,advance='no') 'G'
else if(j.eq.x .and. (i.eq.(y-1).or.i.eq.(y+1))) then
write(*,cfmt,advance='no') 'G'
else if(i.eq.y .and. (j.eq.(x-2).or.j.eq.(x+2))) then
write(*,cfmt,advance='no') '#'
else if(j.eq.x .and. (i.eq.(y-2).or.i.eq.(y+2))) then
write(*,cfmt,advance='no') 'G'
else if((i.eq.(y+1).and.j.eq.(x+1)) .or. (i.eq.(y-1).and.j.eq.(x-1))) then
write(*,cfmt,advance='no') '#'
else if((i.eq.(y+1).and.j.eq.(x-1)) .or. (i.eq.(y-1).and.j.eq.(x+1))) then
write(*,cfmt,advance='no') '#'
else if(j.eq.50) then
write(*,cfmt,advance='no') '|'
else if(i.eq.2) then
write(*,cfmt,advance='no') '-'
else
write(*,cfmt,advance='no') ' '
end if
end do
write(*,*)
end do
end subroutine
A small preview (truncated to a few steps of the pendulum changing direction). Initial angle provided = 80 degrees.
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=={{header|F_Sharp|F#}}== A nice application of F#'s support for units of measure.
open System open System.Drawing open System.Windows.Forms // define units of measurement [<Measure>] type m; // metres [<Measure>] type s; // seconds // a pendulum is represented as a record of physical quantities type Pendulum = { length : float<m> gravity : float<m/s^2> velocity : float<m/s> angle : float } // calculate the next state of a pendulum let next pendulum deltaT : Pendulum = let k = -pendulum.gravity / pendulum.length let acceleration = k * Math.Sin pendulum.angle * 1.0<m> let newVelocity = pendulum.velocity + acceleration * deltaT let newAngle = pendulum.angle + newVelocity * deltaT / 1.0<m> { pendulum with velocity = newVelocity; angle = newAngle } // paint a pendulum (using hard-coded screen coordinates) let paint pendulum (gr: System.Drawing.Graphics) = let homeX = 160 let homeY = 50 let length = 140.0 // draw plate gr.DrawLine( new Pen(Brushes.Gray, width=2.0f), 0, homeY, 320, homeY ) // draw pivot gr.FillEllipse( Brushes.Gray, homeX-5, homeY-5, 10, 10 ) gr.DrawEllipse( new Pen(Brushes.Black), homeX-5, homeY-5, 10, 10 ) // draw the pendulum itself let x = homeX + int( length * Math.Sin pendulum.angle ) let y = homeY + int( length * Math.Cos pendulum.angle ) // draw rod gr.DrawLine( new Pen(Brushes.Black, width=3.0f), homeX, homeY, x, y ) // draw bob gr.FillEllipse( Brushes.Yellow, x-15, y-15, 30, 30 ) gr.DrawEllipse( new Pen(Brushes.Black), x-15, y-15, 30, 30 ) // defines an operator "-?" that calculates the time from t2 to t1 // where t2 is optional let (-?) (t1: DateTime) (t2: DateTime option) : float<s> = match t2 with | None -> 0.0<s> // only one timepoint given -> difference is 0 | Some t -> (t1 - t).TotalSeconds * 1.0<s> // our main window is double-buffered form that reacts to paint events type PendulumForm() as self = inherit Form(Width=325, Height=240, Text="Pendulum") let mutable pendulum = { length = 1.0<m>; gravity = 9.81<m/s^2> velocity = 0.0<m/s> angle = Math.PI / 2.0 } let mutable lastPaintedAt = None let updateFreq = 0.01<s> do self.DoubleBuffered <- true self.Paint.Add( fun args -> let now = DateTime.Now let deltaT = now -? lastPaintedAt |> min 0.01<s> lastPaintedAt <- Some now pendulum <- next pendulum deltaT let gr = args.Graphics gr.Clear( Color.LightGray ) paint pendulum gr // initiate a new paint event after a while (non-blocking) async { do! Async.Sleep( int( 1000.0 * updateFreq / 1.0<s> ) ) self.Invalidate() } |> Async.Start ) [<STAThread>] Application.Run( new PendulumForm( Visible=true ) )
Go
Using {{libheader|GXUI}} from [https://github.com/google/gxui Github]
package main import ( "github.com/google/gxui" "github.com/google/gxui/drivers/gl" "github.com/google/gxui/math" "github.com/google/gxui/themes/dark" omath "math" "time" ) //Two pendulums animated //Top: Mathematical pendulum with small-angle approxmiation (not appropiate with PHI_ZERO=pi/2) //Bottom: Simulated with differential equation phi'' = g/l * sin(phi) const ( ANIMATION_WIDTH int = 480 ANIMATION_HEIGHT int = 320 BALL_RADIUS float32 = 25.0 METER_PER_PIXEL float64 = 1.0 / 20.0 PHI_ZERO float64 = omath.Pi * 0.5 ) var ( l float64 = float64(ANIMATION_HEIGHT) * 0.5 freq float64 = omath.Sqrt(9.81 / (l * METER_PER_PIXEL)) ) type Pendulum interface { GetPhi() float64 } type mathematicalPendulum struct { start time.Time } func (p *mathematicalPendulum) GetPhi() float64 { if (p.start == time.Time{}) { p.start = time.Now() } t := float64(time.Since(p.start).Nanoseconds()) / omath.Pow10(9) return PHI_ZERO * omath.Cos(t*freq) } type numericalPendulum struct { currentPhi float64 angAcc float64 angVel float64 lastTime time.Time } func (p *numericalPendulum) GetPhi() float64 { dt := 0.0 if (p.lastTime != time.Time{}) { dt = float64(time.Since(p.lastTime).Nanoseconds()) / omath.Pow10(9) } p.lastTime = time.Now() p.angAcc = -9.81 / (float64(l) * METER_PER_PIXEL) * omath.Sin(p.currentPhi) p.angVel += p.angAcc * dt p.currentPhi += p.angVel * dt return p.currentPhi } func draw(p Pendulum, canvas gxui.Canvas, x, y int) { attachment := math.Point{X: ANIMATION_WIDTH/2 + x, Y: y} phi := p.GetPhi() ball := math.Point{X: x + ANIMATION_WIDTH/2 + math.Round(float32(l*omath.Sin(phi))), Y: y + math.Round(float32(l*omath.Cos(phi)))} line := gxui.Polygon{gxui.PolygonVertex{attachment, 0}, gxui.PolygonVertex{ball, 0}} canvas.DrawLines(line, gxui.DefaultPen) m := math.Point{int(BALL_RADIUS), int(BALL_RADIUS)} rect := math.Rect{ball.Sub(m), ball.Add(m)} canvas.DrawRoundedRect(rect, BALL_RADIUS, BALL_RADIUS, BALL_RADIUS, BALL_RADIUS, gxui.TransparentPen, gxui.CreateBrush(gxui.Yellow)) } func appMain(driver gxui.Driver) { theme := dark.CreateTheme(driver) window := theme.CreateWindow(ANIMATION_WIDTH, 2*ANIMATION_HEIGHT, "Pendulum") window.SetBackgroundBrush(gxui.CreateBrush(gxui.Gray50)) image := theme.CreateImage() ticker := time.NewTicker(time.Millisecond * 15) pendulum := &mathematicalPendulum{} pendulum2 := &numericalPendulum{PHI_ZERO, 0.0, 0.0, time.Time{}} go func() { for _ = range ticker.C { canvas := driver.CreateCanvas(math.Size{ANIMATION_WIDTH, 2 * ANIMATION_HEIGHT}) canvas.Clear(gxui.White) draw(pendulum, canvas, 0, 0) draw(pendulum2, canvas, 0, ANIMATION_HEIGHT) canvas.Complete() driver.Call(func() { image.SetCanvas(canvas) }) } }() window.AddChild(image) window.OnClose(ticker.Stop) window.OnClose(driver.Terminate) } func main() { gl.StartDriver(appMain) }
Haskell
{{libheader|HGL}}
import Graphics.HGL.Draw.Monad (Graphic, ) import Graphics.HGL.Draw.Picture import Graphics.HGL.Utils import Graphics.HGL.Window import Graphics.HGL.Run import Control.Exception (bracket, ) import Control.Arrow toInt = fromIntegral.round pendulum = runGraphics $ bracket (openWindowEx "Pendulum animation task" Nothing (600,400) DoubleBuffered (Just 30)) closeWindow (\w -> mapM_ ((\ g -> setGraphic w g >> getWindowTick w). (\ (x, y) -> overGraphic (line (300, 0) (x, y)) (ellipse (x - 12, y + 12) (x + 12, y - 12)) )) pts) where dt = 1/30 t = - pi/4 l = 1 g = 9.812 nextAVT (a,v,t) = (a', v', t + v' * dt) where a' = - (g / l) * sin t v' = v + a' * dt pts = map (\(_,t,_) -> (toInt.(300+).(300*).cos &&& toInt. (300*).sin) (pi/2+0.6*t) ) $ iterate nextAVT (- (g / l) * sin t, t, 0)
Usage with ghci:
*Main> pendulum
Alternative solution
{{libheader|Gloss}}
import Graphics.Gloss -- Initial conditions g_ = (-9.8) :: Float --Gravity acceleration v_0 = 0 :: Float --Initial tangential speed a_0 = 0 / 180 * pi :: Float --Initial angle dt = 0.01 :: Float --Time step t_f = 15 :: Float --Final time for data logging l_ = 200 :: Float --Rod length -- Define a type to represent the pendulum: type Pendulum = (Float, Float, Float) -- (rod length, tangential speed, angle) -- Pendulum's initial state initialstate :: Pendulum initialstate = (l_, v_0, a_0) -- Step funtion: update pendulum to new position movePendulum :: Float -> Pendulum -> Pendulum movePendulum dt (l,v,a) = ( l , v_2 , a + v_2 / l * dt*10 ) where v_2 = v + g_ * (cos a) * dt -- Convert from Pendulum to [Picture] for display renderPendulum :: Pendulum -> [Picture] renderPendulum (l,v,a) = map (uncurry Translate newOrigin) [ Line [ ( 0 , 0 ) , ( l * (cos a), l * (sin a) ) ] , polygon [ ( 0 , 0 ) , ( -5 , 8.66 ) , ( 5 , 8.66 ) ] , Translate ( l * (cos a)) (l * (sin a)) (circleSolid (0.04*l_)) , Translate (-1.1*l) (-1.3*l) (Scale 0.1 0.1 (Text currSpeed)) , Translate (-1.1*l) (-1.3*l + 20) (Scale 0.1 0.1 (Text currAngle)) ] where currSpeed = "Speed (pixels/s) = " ++ (show v) currAngle = "Angle (deg) = " ++ (show ( 90 + a / pi * 180 ) ) -- New origin to beter display the animation newOrigin = (0, l_ / 2) -- Calcule a proper window size (for angles between 0 and -pi) windowSize :: (Int, Int) windowSize = ( 300 + 2 * round (snd newOrigin) , 200 + 2 * round (snd newOrigin) ) -- Run simulation main :: IO () main = do --plotOnGNU simulate window background fps initialstate render update where window = InWindow "Animate a pendulum" windowSize (40, 40) background = white fps = round (1/dt) render xs = pictures $ renderPendulum xs update _ = movePendulum
HicEst
[http://www.HicEst.com/DIFFEQ.htm DIFFEQ] and the callback procedure pendulum numerically integrate the pendulum equation. The display window can be resized during the run, but for window width not equal to 2*height the pendulum rod becomes a rubber band instead:
REAL :: msec=10, Lrod=1, dBob=0.03, g=9.81, Theta(2), dTheta(2)
BobMargins = ALIAS(ls, rs, ts, bs) ! box margins to draw the bob
Theta = (1, 0) ! initial angle and velocity
start_t = TIME()
DO i = 1, 1E100 ! "forever"
end_t = TIME() ! to integrate in real-time sections:
DIFFEQ(Callback="pendulum", T=end_t, Y=Theta, DY=dTheta, T0=start_t)
xBob = (SIN(Theta(1)) + 1) / 2
yBob = COS(Theta(1)) - dBob
! create or clear window and draw pendulum bob at (xBob, yBob):
WINDOW(WIN=wh, LeftSpace=0, RightSpace=0, TopSpace=0, BottomSpace=0, Up=999)
BobMargins = (xBob-dBob, 1-xBob-dBob, yBob-dBob, 1-yBob-dBob)
WINDOW(WIN=wh, LeftSpace=ls, RightSpace=rs, TopSpace=ts, BottomSpace=bs)
WRITE(WIN=wh, DeCoRation='EL=4, BC=4') ! flooded red ellipse as bob
! draw the rod hanging from the center of the window:
WINDOW(WIN=wh, LeftSpace=0.5, TopSpace=0, RightSpace=rs+dBob)
WRITE(WIN=wh, DeCoRation='LI=0 0; 1 1, FC=4.02') ! red pendulum rod
SYSTEM(WAIT=msec)
start_t = end_t
ENDDO
END
SUBROUTINE pendulum ! Theta" = - (g/Lrod) * SIN(Theta)
dTheta(1) = Theta(2) ! Theta' = Theta(2) substitution
dTheta(2) = -g/Lrod*SIN(Theta(1)) ! Theta" = Theta(2)' = -g/Lrod*SIN(Theta(1))
END
== Icon and {{header|Unicon}} ==
The following code uses features exclusive to Unicon, specifically the object-oriented gui library.
{{trans|Scheme}}
import gui
$include "guih.icn"
# some constants to define the display and pendulum
$define HEIGHT 400
$define WIDTH 500
$define STRING_LENGTH 200
$define HOME_X 250
$define HOME_Y 21
$define SIZE 30
$define START_ANGLE 80
class WindowApp : Dialog ()
# draw the pendulum on given context_window, at position (x,y)
method draw_pendulum (x, y)
# reference to current screen area to draw on
cw := Clone(self.cwin)
# clear screen
WAttrib (cw, "bg=grey")
EraseRectangle (cw, 0, 0, WIDTH, HEIGHT)
# draw the display
WAttrib (cw, "fg=dark gray")
DrawLine (cw, 10, 20, WIDTH-20, 20)
WAttrib (cw, "fg=black")
DrawLine (cw, HOME_X, HOME_Y, x, y)
FillCircle (cw, x, y, SIZE+2)
WAttrib (cw, "fg=yellow")
FillCircle (cw, x, y, SIZE)
# free reference to screen area
Uncouple (cw)
end
# find the average of given two arguments
method avg (a, b)
return (a + b) / 2
end
# this method gets called by the ticker
# it computes the next position of the pendulum and
# requests a redraw
method tick ()
static x, y
static theta := START_ANGLE
static d_theta := 0
# update x,y of pendulum
scaling := 3000.0 / (STRING_LENGTH * STRING_LENGTH)
# -- first estimate
first_dd_theta := -(sin (dtor (theta)) * scaling)
mid_d_theta := d_theta + first_dd_theta
mid_theta := theta + avg (d_theta, mid_d_theta)
# -- second estimate
mid_dd_theta := - (sin (dtor (mid_theta)) * scaling)
mid_d_theta_2 := d_theta + avg (first_dd_theta, mid_dd_theta)
mid_theta_2 := theta + avg (d_theta, mid_d_theta_2)
# -- again first
mid_dd_theta_2 := -(sin (dtor (mid_theta_2)) * scaling)
last_d_theta := mid_d_theta_2 + mid_dd_theta_2
last_theta := mid_theta_2 + avg (mid_d_theta_2, last_d_theta)
# -- again second
last_dd_theta := - (sin (dtor (last_theta)) * scaling)
last_d_theta_2 := mid_d_theta_2 + avg (mid_dd_theta_2, last_dd_theta)
last_theta_2 := mid_theta_2 + avg (mid_d_theta_2, last_d_theta_2)
# -- update stored angles
d_theta := last_d_theta_2
theta := last_theta_2
# -- update x, y
pendulum_angle := dtor (theta)
x := HOME_X + STRING_LENGTH * sin (pendulum_angle)
y := HOME_Y + STRING_LENGTH * cos (pendulum_angle)
# draw pendulum
draw_pendulum (x, y)
end
# set up the window
method component_setup ()
# some cosmetic settings for the window
attrib("size="||WIDTH||","||HEIGHT, "bg=light gray", "label=Pendulum")
# make sure we respond to window close event
connect (self, "dispose", CLOSE_BUTTON_EVENT)
# start the ticker, to update the display periodically
self.set_ticker (20)
end
end
procedure main ()
w := WindowApp ()
w.show_modal ()
end
J
Works for '''J6'''
require 'gl2 trig'
coinsert 'jgl2'
DT =: %30 NB. seconds
ANGLE=: 0.45p1 NB. radians
L =: 1 NB. metres
G =: 9.80665 NB. ms_2
VEL =: 0 NB. ms_1
PEND=: noun define
pc pend;pn "Pendulum";
xywh 0 0 320 200;cc isi isigraph rightmove bottommove;
pas 0 0;pcenter;
rem form end;
)
pend_run =: verb def ' wd PEND,'';pshow;timer '',":DT * 1000 '
pend_close =: verb def ' wd ''timer 0; pclose'' '
pend_isi_paint=: verb def ' drawPendulum ANGLE '
sys_timer_z_=: verb define
recalcAngle ''
wd 'psel pend; setinvalid isi'
)
recalcAngle=: verb define
accel=. - (G % L) * sin ANGLE
VEL =: VEL + accel * DT
ANGLE=: ANGLE + VEL * DT
)
drawPendulum=: verb define
width=. {. glqwh''
ps=. (-: width) , 40
pe=. ps + 280 <.@* (cos , sin) 0.5p1 + y NB. adjust orientation
glbrush glrgb 91 91 91
gllines ps , pe
glellipse (,~ ps - -:) 40 15
glellipse (,~ pe - -:) 20 20
glrect 0 0 ,width, 40
)
pend_run'' NB. run animation
Updated for changes in '''J8'''
require 'gl2 trig'
coinsert 'jgl2'
DT =: %30 NB. seconds
ANGLE=: 0.45p1 NB. radians
L =: 1 NB. metres
G =: 9.80665 NB. ms_2
VEL =: 0 NB. ms_1
PEND=: noun define
pc pend;pn "Pendulum";
minwh 320 200; cc isi isigraph flush;
)
pend_run=: verb define
wd PEND,'pshow'
wd 'timer ',":DT * 1000
)
pend_close=: verb define
wd 'timer 0; pclose'
)
sys_timer_z_=: verb define
recalcAngle_base_ ''
wd 'psel pend; set isi invalid'
)
pend_isi_paint=: verb define
drawPendulum ANGLE
)
recalcAngle=: verb define
accel=. - (G % L) * sin ANGLE
VEL =: VEL + accel * DT
ANGLE=: ANGLE + VEL * DT
)
drawPendulum=: verb define
width=. {. glqwh''
ps=. (-: width) , 20
pe=. ps + 150 <.@* (cos , sin) 0.5p1 + y NB. adjust orientation
glclear''
glbrush glrgb 91 91 91 NB. gray
gllines ps , pe
glellipse (,~ ps - -:) 40 15
glrect 0 0, width, 20
glbrush glrgb 255 255 0 NB. yellow
glellipse (,~ pe - -:) 15 15 NB. orb
)
pend_run''
[[File:J_pendulum.gif|320px|pretend the ball is yellow - gifgrabber grabbed a monochrome image for some reason...]]
Java
{{libheader|Swing}} {{libheader|AWT}}
import java.awt.*; import javax.swing.*; public class Pendulum extends JPanel implements Runnable { private double angle = Math.PI / 2; private int length; public Pendulum(int length) { this.length = length; setDoubleBuffered(true); } @Override public void paint(Graphics g) { g.setColor(Color.WHITE); g.fillRect(0, 0, getWidth(), getHeight()); g.setColor(Color.BLACK); int anchorX = getWidth() / 2, anchorY = getHeight() / 4; int ballX = anchorX + (int) (Math.sin(angle) * length); int ballY = anchorY + (int) (Math.cos(angle) * length); g.drawLine(anchorX, anchorY, ballX, ballY); g.fillOval(anchorX - 3, anchorY - 4, 7, 7); g.fillOval(ballX - 7, ballY - 7, 14, 14); } public void run() { double angleAccel, angleVelocity = 0, dt = 0.1; while (true) { angleAccel = -9.81 / length * Math.sin(angle); angleVelocity += angleAccel * dt; angle += angleVelocity * dt; repaint(); try { Thread.sleep(15); } catch (InterruptedException ex) {} } } @Override public Dimension getPreferredSize() { return new Dimension(2 * length + 50, length / 2 * 3); } public static void main(String[] args) { JFrame f = new JFrame("Pendulum"); Pendulum p = new Pendulum(200); f.add(p); f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); f.pack(); f.setVisible(true); new Thread(p).start(); } }
JavaScript
===With <canvas>=== {{trans|E}} (plus gratuitous motion blur)
<title>Pendulum</title>
</head><body style="background: gray;">
<canvas id="canvas" width="600" height="600">
<p>Sorry, your browser does not support the <canvas> used to display the pendulum animation.</p>
</canvas>
<script>
function PendulumSim(length_m, gravity_mps2, initialAngle_rad, timestep_ms, callback) {
var velocity = 0;
var angle = initialAngle_rad;
var k = -gravity_mps2/length_m;
var timestep_s = timestep_ms / 1000;
return setInterval(function () {
var acceleration = k * Math.sin(angle);
velocity += acceleration * timestep_s;
angle += velocity * timestep_s;
callback(angle);
}, timestep_ms);
}
var canvas = document.getElementById('canvas');
var context = canvas.getContext('2d');
var prev=0;
var sim = PendulumSim(1, 9.80665, Math.PI*99/100, 10, function (angle) {
var rPend = Math.min(canvas.width, canvas.height) * 0.47;
var rBall = Math.min(canvas.width, canvas.height) * 0.02;
var rBar = Math.min(canvas.width, canvas.height) * 0.005;
var ballX = Math.sin(angle) * rPend;
var ballY = Math.cos(angle) * rPend;
context.fillStyle = "rgba(255,255,255,0.51)";
context.globalCompositeOperation = "destination-out";
context.fillRect(0, 0, canvas.width, canvas.height);
context.fillStyle = "yellow";
context.strokeStyle = "rgba(0,0,0,"+Math.max(0,1-Math.abs(prev-angle)*10)+")";
context.globalCompositeOperation = "source-over";
context.save();
context.translate(canvas.width/2, canvas.height/2);
context.rotate(angle);
context.beginPath();
context.rect(-rBar, -rBar, rBar*2, rPend+rBar*2);
context.fill();
context.stroke();
context.beginPath();
context.arc(0, rPend, rBall, 0, Math.PI*2, false);
context.fill();
context.stroke();
context.restore();
prev=angle;
});
</script>
</body></html>
===With <SVG>=== With some control elements to ease the usage.
<head>
<title>Swinging Pendulum Simulation</title>
</head>
<body><center>
<svg id="scene" height="200" width="300">
<line id="string" x1="150" y1="50" x2="250" y2="50" stroke="brown" stroke-width="4" />
<circle id="ball" cx="250" cy="50" r="20" fill="black" />
</svg>
Initial angle:<input id="in_angle" type="number" min="0" max="180" onchange="condReset()"/>(degrees)
<button type="button" onclick="startAnimation()">Start</button>
<button type="button" onclick="stopAnimation()">Stop</button>
<button type="button" onclick="reset()">Reset</button>
<script>
in_angle.value = 0;
var cx = 150, cy = 50;
var radius = 100; // cm
var g = 9.81; // m/s^2
var angle = 0; // radians
var vel = 0; // m/s
var dx = 0.02; // s
var acc, vel, penx, peny;
var timerFunction = null;
function stopAnimation() {
if(timerFunction != null){
clearInterval(timerFunction);
timerFunction = null;
}
}
function startAnimation() {
if(!timerFunction) timerFunction = setInterval(swing, dx * 1000);
}
function swing(){
acc = g * Math.cos(angle);
vel += acc * dx;//Convert m/s/s to m/s
angle += vel/(radius/100) * dx; //convert m/s into rad/s and then into rad
setPenPos();
}
function setPenPos(){
penx = cx + radius * Math.cos(angle);
peny = cy + radius * Math.sin(angle);
scene.getElementById("string").setAttribute("x2", penx);
scene.getElementById("string").setAttribute("y2", peny);
scene.getElementById("ball").setAttribute("cx", penx);
scene.getElementById("ball").setAttribute("cy", peny);
}
function reset(){
var val = parseInt(in_angle.value)*0.0174532925199;
if (val) angle = val;
else angle = 0;
acc = 0;
vel = 0;
setPenPos();
}
function condReset(){
if (!timerFunction) reset();
}
</script>
</body>
</html>
Julia
Differential equation based solution using the Luxor graphics library.
using Luxor using Colors using BoundaryValueDiffEq # constants for differential equations and movie const g = 9.81 const L = 1.0 # pendulum length in meters const bobd = 0.10 # pendulum bob diameter in meters const framerate = 50.0 # intended frame rate/sec const t0 = 0.0 # start time (s) const tf = 2.3 # end simulation time (s) const dtframe = 1.0/framerate # time increment per frame const tspan = LinRange(t0, tf, Int(floor(tf*framerate))) # array of time points in animation const bgcolor = "black" # gif background const leaderhue = (0.80, 0.70, 0.20) # gif swing arm hue light gold const hslcolors = [HSL(col) for col in (distinguishable_colors( Int(floor(tf*framerate)+3),[RGB(1,1,1)])[2:end])] const giffilename = "pendulum.gif" # output file # differential equations simplependulum(du, u, p, t) = (θ=u[1]; dθ=u[2]; du[1]=dθ; du[2]=-(g/L)*sin(θ)) bc2(residual, u, p, t) = (residual[1] = u[end÷2][1] + pi/2; residual[2] = u[end][1] - pi/2) bvp2 = BVProblem(simplependulum, bc2, [pi/2,pi/2], (tspan[1],tspan[end])) sol2 = solve(bvp2, MIRK4(), dt=dtframe) # use the MIRK4 solver for TwoPointBVProblem # movie making background backdrop(scene, framenumber) = background(bgcolor) function frame(scene, framenumber) u1, u2 = sol2.u[framenumber] y, x = L*cos(u1), L*sin(u1) sethue(leaderhue) poly([Point(-4.0, 0.0), Point(4.0, 0.0), Point(160.0x,160.0y)], :fill) sethue(Colors.HSV(framenumber*4.0, 1, 1)) circle(Point(160.0x,160.0y), 160bobd, :fill) text(string("frame $framenumber of $(scene.framerange.stop)"), Point(0.0, -190.0), halign=:center) end muv = Movie(400, 400, "Pendulum Demo", 1:length(tspan)) animate(muv, [Scene(muv, backdrop), Scene(muv, frame, easingfunction=easeinoutcubic)], creategif=true, pathname=giffilename)
Kotlin
Conversion of Java snippet.
import java.awt.* import java.util.concurrent.* import javax.swing.* class Pendulum(private val length: Int) : JPanel(), Runnable { init { val f = JFrame("Pendulum") f.add(this) f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE f.pack() f.isVisible = true isDoubleBuffered = true } override fun paint(g: Graphics) { with(g) { color = Color.WHITE fillRect(0, 0, width, height) color = Color.BLACK val anchor = Element(width / 2, height / 4) val ball = Element((anchor.x + Math.sin(angle) * length).toInt(), (anchor.y + Math.cos(angle) * length).toInt()) drawLine(anchor.x, anchor.y, ball.x, ball.y) fillOval(anchor.x - 3, anchor.y - 4, 7, 7) fillOval(ball.x - 7, ball.y - 7, 14, 14) } } override fun run() { angleVelocity += -9.81 / length * Math.sin(angle) * dt angle += angleVelocity * dt repaint() } override fun getPreferredSize() = Dimension(2 * length + 50, length / 2 * 3) private data class Element(val x: Int, val y: Int) private val dt = 0.1 private var angle = Math.PI / 2 private var angleVelocity = 0.0 } fun main(a: Array<String>) { val executor = Executors.newSingleThreadScheduledExecutor() executor.scheduleAtFixedRate(Pendulum(200), 0, 15, TimeUnit.MILLISECONDS) }
Liberty BASIC
nomainwin
WindowWidth = 400
WindowHeight = 300
open "Pendulum" for graphics_nsb_nf as #main
#main "down;fill white; flush"
#main "color black"
#main "trapclose [quit.main]"
Angle = asn(1)
DeltaT = 0.1
PendLength = 150
FixX = int(WindowWidth / 2)
FixY = 40
timer 30, [swing]
wait
[swing]
#main "cls"
#main "discard"
PlumbobX = FixX + int(sin(Angle) * PendLength)
PlumbobY = FixY + int(cos(Angle) * PendLength)
AngAccel = -9.81 / PendLength * sin(Angle)
AngVelocity = AngVelocity + AngAccel * DeltaT
Angle = Angle + AngVelocity * DeltaT
#main "backcolor black"
#main "place ";FixX;" ";FixY
#main "circlefilled 3"
#main "line ";FixX;" ";FixY;" ";PlumbobX;" ";PlumbobY
#main "backcolor red"
#main "circlefilled 10"
wait
[quit.main]
close #main
end
Lingo
global RODLEN, GRAVITY, DT
global velocity, acceleration, angle, posX, posY
on startMovie
-- window properties
_movie.stage.title = "Pendulum"
_movie.stage.titlebarOptions.visible = TRUE
_movie.stage.rect = rect(0, 0, 400, 400)
_movie.centerStage = TRUE
_movie.puppetTempo(30)
RODLEN = 180
GRAVITY = -9.8
DT = 0.03
velocity = 0.0
acceleration = 0.0
angle = PI/3
posX = 200 - sin(angle) * RODLEN
posY = 100 + cos(angle) * RODLEN
paint()
-- show the window
_movie.stage.visible = TRUE
end
on enterFrame
acceleration = GRAVITY * sin(angle)
velocity = velocity + acceleration * DT
angle = angle + velocity * DT
posX = 200 - sin(angle) * rodLen
posY = 100 + cos(angle) * rodLen
paint()
end
on paint
img = _movie.stage.image
img.fill(img.rect, rgb(255,255,255))
img.fill(point(200-5, 100-5), point(200+5, 100+5), [#shapeType:#oval,#color:rgb(0,0,0)])
img.draw(point(200, 100), point(posX, posY), [#color:rgb(0,0,0)])
img.fill(point(posX-20, posY-20), point(posX+20, posY+20), [#shapeType:#oval,#lineSize:1,#bgColor:rgb(0,0,0),#color:rgb(255,255,0)])
end
Logo
{{works with|UCB Logo}}
make "angle 45
make "L 1
make "bob 10
to draw.pendulum
clearscreen
seth :angle+180 ; down on screen is 180
forward :L*100-:bob
penup
forward :bob
pendown
arc 360 :bob
end
make "G 9.80665
make "dt 1/30
make "acc 0
make "vel 0
to step.pendulum
make "acc -:G / :L * sin :angle
make "vel :vel + :acc * :dt
make "angle :angle + :vel * :dt
wait :dt*60
draw.pendulum
end
hideturtle
until [key?] [step.pendulum]
Lua
Needs LÖVE 2D Engine
function degToRad( d ) return d * 0.01745329251 end function love.load() g = love.graphics rodLen, gravity, velocity, acceleration = 260, 3, 0, 0 halfWid, damp = g.getWidth() / 2, .989 posX, posY, angle = halfWid TWO_PI, angle = math.pi * 2, degToRad( 90 ) end function love.update( dt ) acceleration = -gravity / rodLen * math.sin( angle ) angle = angle + velocity; if angle > TWO_PI then angle = 0 end velocity = velocity + acceleration velocity = velocity * damp posX = halfWid + math.sin( angle ) * rodLen posY = math.cos( angle ) * rodLen end function love.draw() g.setColor( 250, 0, 250 ) g.circle( "fill", halfWid, 0, 8 ) g.line( halfWid, 4, posX, posY ) g.setColor( 250, 100, 20 ) g.circle( "fill", posX, posY, 20 ) end
M2000 Interpreter
Module Pendulum {
back()
degree=180/pi
THETA=Pi/2
SPEED=0
G=9.81
L=0.5
Profiler
lasttimecount=0
cc=40 ' 40 ms every draw
accold=0
Every cc {
ACCEL=G*SIN(THETA*degree)/L/50
SPEED+=ACCEL/cc
THETA+=SPEED
Pendulum(THETA)
if KeyPress(32) Then Exit
}
Sub back()
If not IsWine then Smooth On
Cls 7,0
Pen 0
Move 0, scale.y/4
Draw scale.x,0
Step -scale.x/2
circle fill #AAAAAA, scale.x/50
Hold ' hold this as background
End Sub
Sub Pendulum(x)
x+=pi/2
Release ' place stored background to screen
Width scale.x/2000 {
Draw Angle x, scale.y/2.5
Width 1 {
Circle Fill 14, scale.x/25
}
Step Angle x, -scale.y/2.5
}
Print @(1,1), lasttimecount
if sgn(accold)<>sgn(ACCEL) then lasttimecount=timecount: Profiler
accold=ACCEL
Refresh 1000
End Sub
}
Pendulum
=={{header|Mathematica}} / {{header|Wolfram Language}}==
freq = 8; length = freq^(-1/2);
Animate[Graphics[
List[{Line[{{0, 0}, length {Sin[T], -Cos[T]}} /. {T -> (Pi/6) Cos[2 Pi freq t]}], PointSize[Large],
Point[{length {Sin[T], -Cos[T]}} /. {T -> (Pi/6) Cos[2 Pi freq t]}]}],
PlotRange -> {{-0.3, 0.3}, {-0.5, 0}}], {t, 0, 1}, AnimationRate -> 0.07]
[[File:mmapendulum.gif]]
MATLAB
pendulum.m
%This is a numerical simulation of a pendulum with a massless pivot arm. %% User Defined Parameters %Define external parameters g = -9.8; deltaTime = 1/50; %Decreasing this will increase simulation accuracy endTime = 16; %Define pendulum rodPivotPoint = [2 2]; %rectangular coordinates rodLength = 1; mass = 1; %of the bob radius = .2; %of the bob theta = 45; %degrees, defines initial position of the bob velocity = [0 0]; %cylindrical coordinates; first entry is radial velocity, %second entry is angular velocity %% Simulation assert(radius < rodLength,'Pendulum bob radius must be less than the length of the rod.'); position = rodPivotPoint - (rodLength*[-sind(theta) cosd(theta)]); %in rectangular coordinates %Generate graphics, render pendulum figure; axesHandle = gca; xlim(axesHandle, [(rodPivotPoint(1) - rodLength - radius) (rodPivotPoint(1) + rodLength + radius)] ); ylim(axesHandle, [(rodPivotPoint(2) - rodLength - radius) (rodPivotPoint(2) + rodLength + radius)] ); rectHandle = rectangle('Position',[(position - radius/2) radius radius],... 'Curvature',[1,1],'FaceColor','g'); %Pendulum bob hold on plot(rodPivotPoint(1),rodPivotPoint(2),'^'); %pendulum pivot lineHandle = line([rodPivotPoint(1) position(1)],... [rodPivotPoint(2) position(2)]); %pendulum rod hold off %Run simulation, all calculations are performed in cylindrical coordinates for time = (deltaTime:deltaTime:endTime) drawnow; %Forces MATLAB to render the pendulum %Find total force gravitationalForceCylindrical = [mass*g*cosd(theta) mass*g*sind(theta)]; %This code is just incase you want to add more forces,e.g friction totalForce = gravitationalForceCylindrical; %If the rod isn't massless or is a spring, etc., modify this line %accordingly rodForce = [-totalForce(1) 0]; %cylindrical coordinates totalForce = totalForce + rodForce; acceleration = totalForce / mass; %F = ma velocity = velocity + acceleration * deltaTime; rodLength = rodLength + velocity(1) * deltaTime; theta = theta + velocity(2) * deltaTime; % Attention!! Mistake here. % Velocity needs to be divided by pendulum length and scaled to degrees: % theta = theta + velocity(2) * deltaTime/rodLength/pi*180; position = rodPivotPoint - (rodLength*[-sind(theta) cosd(theta)]); %Update figure with new position info set(rectHandle,'Position',[(position - radius/2) radius radius]); set(lineHandle,'XData',[rodPivotPoint(1) position(1)],'YData',... [rodPivotPoint(2) position(2)]); end
ooRexx
ooRexx does not have a portable GUI, but this version is similar to the Ada version and just prints out the coordinates of the end of the pendulum.
pendulum = .pendulum~new(10, 30)
before = .datetime~new
do 100 -- somewhat arbitrary loop count
call syssleep .2
now = .datetime~new
pendulum~update(now - before)
before = now
say " X:" pendulum~x " Y:" pendulum~y
end
::class pendulum
::method init
expose length theta x y velocity
use arg length, theta
x = rxcalcsin(theta) * length
y = rxcalccos(theta) * length
velocity = 0
::attribute x GET
::attribute y GET
::constant g -9.81 -- acceleration due to gravity
::method update
expose length theta x y velocity
use arg duration
acceleration = self~g / length * rxcalcsin(theta)
durationSeconds = duration~microseconds / 1000000
x = rxcalcsin(theta, length)
y = rxcalccos(theta, length)
velocity = velocity + acceleration * durationSeconds
theta = theta + velocity * durationSeconds
::requires rxmath library
Oz
Inspired by the E and Ruby versions.
declare
[QTk] = {Link ['x-oz://system/wp/QTk.ozf']}
Pi = 3.14159265
class PendulumModel
feat
K
attr
angle
velocity
meth init(length:L <= 1.0 %% meters
gravity:G <= 9.81 %% m/s²
initialAngle:A <= Pi/2.) %% radians
self.K = ~G / L
angle := A
velocity := 0.0
end
meth nextAngle(deltaT:DeltaTMS %% milliseconds
?Angle) %% radians
DeltaT = {Int.toFloat DeltaTMS} / 1000.0 %% seconds
Acceleration = self.K * {Sin @angle}
in
velocity := @velocity + Acceleration * DeltaT
angle := @angle + @velocity * DeltaT
Angle = @angle
end
end
%% Animates a pendulum on a given canvas.
class PendulumAnimation from Time.repeat
feat
Pend
Rod
Bob
home:pos(x:160 y:50)
length:140.0
delay
meth init(Pendulum Canvas delay:Delay <= 25) %% milliseconds
self.Pend = Pendulum
self.delay = Delay
%% plate and pivot
{Canvas create(line 0 self.home.y 320 self.home.y width:2 fill:grey50)}
{Canvas create(oval 155 self.home.y-5 165 self.home.y+5 fill:grey50 outline:black)}
%% the pendulum itself
self.Rod = {Canvas create(line 1 1 1 1 width:3 fill:black handle:$)}
self.Bob = {Canvas create(oval 1 1 2 2 fill:yellow outline:black handle:$)}
%%
{self setRepAll(action:Animate delay:Delay)}
end
meth Animate
Theta = {self.Pend nextAngle(deltaT:self.delay $)}
%% calculate x and y from angle
X = self.home.x + {Float.toInt self.length * {Sin Theta}}
Y = self.home.y + {Float.toInt self.length * {Cos Theta}}
in
%% update canvas
try
{self.Rod setCoords(self.home.x self.home.y X Y)}
{self.Bob setCoords(X-15 Y-15 X+15 Y+15)}
catch system(tk(alreadyClosed ...) ...) then skip end
end
end
Pendulum = {New PendulumModel init}
Canvas
GUI = td(title:"Pendulum"
canvas(width:320 height:210 handle:?Canvas)
action:proc {$} {Animation stop} {Window close} end
)
Window = {QTk.build GUI}
Animation = {New PendulumAnimation init(Pendulum Canvas)}
in
{Window show}
{Animation go}
Perl
{{libheader|Perl/Tk}}
{{trans|Tcl}}
This does not have the window resizing handling that Tcl does.
use strict; use warnings; use Tk; use Math::Trig qw/:pi/; my $root = new MainWindow( -title => 'Pendulum Animation' ); my $canvas = $root->Canvas(-width => 320, -height => 200); my $after_id; for ($canvas) { $_->createLine( 0, 25, 320, 25, -tags => [qw/plate/], -width => 2, -fill => 'grey50' ); $_->createOval( 155, 20, 165, 30, -tags => [qw/pivot outline/], -fill => 'grey50' ); $_->createLine( 1, 1, 1, 1, -tags => [qw/rod width/], -width => 3, -fill => 'black' ); $_->createOval( 1, 1, 2, 2, -tags => [qw/bob outline/], -fill => 'yellow' ); } $canvas->raise('pivot'); $canvas->pack(-fill => 'both', -expand => 1); my ($Theta, $dTheta, $length, $homeX, $homeY) = (45, 0, 150, 160, 25); sub show_pendulum { my $angle = $Theta * pi() / 180; my $x = $homeX + $length * sin($angle); my $y = $homeY + $length * cos($angle); $canvas->coords('rod', $homeX, $homeY, $x, $y); $canvas->coords('bob', $x-15, $y-15, $x+15, $y+15); } sub recompute_angle { my $scaling = 3000.0 / ($length ** 2); # first estimate my $firstDDTheta = -sin($Theta * pi / 180) * $scaling; my $midDTheta = $dTheta + $firstDDTheta; my $midTheta = $Theta + ($dTheta + $midDTheta)/2; # second estimate my $midDDTheta = -sin($midTheta * pi/ 180) * $scaling; $midDTheta = $dTheta + ($firstDDTheta + $midDDTheta)/2; $midTheta = $Theta + ($dTheta + $midDTheta)/2; # again, first $midDDTheta = -sin($midTheta * pi/ 180) * $scaling; my $lastDTheta = $midDTheta + $midDDTheta; my $lastTheta = $midTheta + ($midDTheta + $lastDTheta)/2; # again, second my $lastDDTheta = -sin($lastTheta * pi/180) * $scaling; $lastDTheta = $midDTheta + ($midDDTheta + $lastDDTheta)/2; $lastTheta = $midTheta + ($midDTheta + $lastDTheta)/2; # Now put the values back in our globals $dTheta = $lastDTheta; $Theta = $lastTheta; } sub animate { recompute_angle; show_pendulum; $after_id = $root->after(15 => sub {animate() }); } show_pendulum; $after_id = $root->after(500 => sub {animate}); $canvas->bind('<Destroy>' => sub {$after_id->cancel}); MainLoop;
Perl 6
{{works with|Rakudo|2018.09}} Handles window resizing, modifies pendulum length and period as window height changes. May need to tweek $ppi scaling to get good looking animation.
use SDL2::Raw;
use Cairo;
my $width = 1000;
my $height = 400;
SDL_Init(VIDEO);
my $window = SDL_CreateWindow(
'Pendulum - Perl 6',
SDL_WINDOWPOS_CENTERED_MASK,
SDL_WINDOWPOS_CENTERED_MASK,
$width, $height, RESIZABLE
);
my $render = SDL_CreateRenderer($window, -1, ACCELERATED +| PRESENTVSYNC);
my $bob = Cairo::Image.create( Cairo::FORMAT_ARGB32, 32, 32 );
given Cairo::Context.new($bob) {
my Cairo::Pattern::Gradient::Radial $sphere .=
create(13.3, 12.8, 3.2, 12.8, 12.8, 32);
$sphere.add_color_stop_rgba(0, 1, 1, .698, 1);
$sphere.add_color_stop_rgba(1, .623, .669, .144, 1);
.pattern($sphere);
.arc(16, 16, 15, 0, 2 * pi);
.fill;
$sphere.destroy;
}
my $bob_texture = SDL_CreateTexture(
$render, %PIXELFORMAT<ARGB8888>,
STATIC, 32, 32
);
SDL_UpdateTexture(
$bob_texture,
SDL_Rect.new(:x(0), :y(0), :w(32), :h(32)),
$bob.data, $bob.stride // 32
);
SDL_SetTextureBlendMode($bob_texture, 1);
SDL_SetRenderDrawBlendMode($render, 1);
my $event = SDL_Event.new;
my $now = now; # time
my $Θ = -π/3; # start angle
my $ppi = 500; # scale
my $g = -9.81; # accelaration of gravity
my $ax = $width/2; # anchor x
my $ay = 25; # anchor y
my $len = $height - 75; # 'rope' length
my $vel; # velocity
my $dt; # delta time
main: loop {
while SDL_PollEvent($event) {
my $casted_event = SDL_CastEvent($event);
given $casted_event {
when *.type == QUIT { last main }
when *.type == WINDOWEVENT {
if .event == 5 {
$width = .data1;
$height = .data2;
$ax = $width/2;
$len = $height - 75;
}
}
}
}
$dt = now - $now;
$now = now;
$vel += $g / $len * sin($Θ) * $ppi * $dt;
$Θ += $vel * $dt;
my $bx = $ax + sin($Θ) * $len;
my $by = $ay + cos($Θ) * $len;
SDL_SetRenderDrawColor($render, 255, 255, 255, 255);
SDL_RenderDrawLine($render, |($ax, $ay, $bx, $by)».round);
SDL_RenderCopy( $render, $bob_texture, Nil,
SDL_Rect.new($bx - 16, $by - 16, 32, 32)
);
SDL_RenderPresent($render);
SDL_SetRenderDrawColor($render, 0, 0, 0, 0);
SDL_RenderClear($render);
}
SDL_Quit();
Phix
{{libheader|pGUI}}
-- demo\rosetta\animate_pendulum2.exw
include pGUI.e
Ihandle dlg, canvas, timer
cdCanvas cdcanvas
constant g = 50
atom angle = PI/2,
velocity = 0
integer w, h, len = 0
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
{w, h} = IupGetIntInt(canvas, "DRAWSIZE")
cdCanvasActivate(cdcanvas)
cdCanvasClear(cdcanvas)
-- new suspension point:
integer sX = floor(w/2)
integer sY = floor(h/16)
-- repaint:
integer eX = floor(len*sin(angle)+sX)
integer eY = floor(len*cos(angle)+sY)
cdCanvasSetForeground(cdcanvas, CD_CYAN)
cdCanvasLine(cdcanvas, sX, h-sY, eX, h-eY)
cdCanvasSetForeground(cdcanvas, CD_DARK_GREEN)
cdCanvasSector(cdcanvas, sX, h-sY, 5, 5, 0, 360)
cdCanvasSetForeground(cdcanvas, CD_BLUE)
cdCanvasSector(cdcanvas, eX, h-eY, 35, 35, 0, 360)
cdCanvasFlush(cdcanvas)
return IUP_DEFAULT
end function
function timer_cb(Ihandle /*ih*/)
integer newlen = floor(w/2)-30
if newlen!=len then
len = newlen
atom tmp = 2*g*len*(cos(angle))
velocity = iff(tmp<0?0:sqrt(tmp)*sign(velocity))
end if
atom dt = 0.2/w
atom delta = -len*sin(angle)*g
velocity += dt*delta
angle += dt*velocity
IupUpdate(canvas)
return IUP_IGNORE
end function
function map_cb(Ihandle ih)
atom res = IupGetDouble(NULL, "SCREENDPI")/25.4
IupGLMakeCurrent(canvas)
cdcanvas = cdCreateCanvas(CD_GL, "10x10 %g", {res})
cdCanvasSetBackground(cdcanvas, CD_PARCHMENT)
return IUP_DEFAULT
end function
function canvas_resize_cb(Ihandle /*canvas*/)
integer {canvas_width, canvas_height} = IupGetIntInt(canvas, "DRAWSIZE")
atom res = IupGetDouble(NULL, "SCREENDPI")/25.4
cdCanvasSetAttribute(cdcanvas, "SIZE", "%dx%d %g", {canvas_width, canvas_height, res})
return IUP_DEFAULT
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
return IUP_CONTINUE
end function
procedure main()
IupOpen()
canvas = IupGLCanvas()
IupSetAttribute(canvas, "RASTERSIZE", "640x380")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupSetCallback(canvas, "RESIZE_CB", Icallback("canvas_resize_cb"))
timer = IupTimer(Icallback("timer_cb"), 20)
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Animated Pendulum")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupShow(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
IupMainLoop()
IupClose()
end procedure
main()
PicoLisp
A minimalist solution. The pendulum consists of the center point '+', and the swinging xterm cursor.
(load "@lib/math.l")
(de pendulum (X Y Len)
(let (Angle pi/2 V 0)
(call 'clear)
(call 'tput "cup" Y X)
(prin '+)
(call 'tput "cup" 1 (+ X Len))
(until (key 25) # 25 ms
(let A (*/ (sin Angle) -9.81 1.0)
(inc 'V (*/ A 40)) # DT = 25 ms = 1/40 sec
(inc 'Angle (*/ V 40)) )
(call 'tput "cup"
(+ Y (*/ Len (cos Angle) 2.2)) # Compensate for aspect ratio
(+ X (*/ Len (sin Angle) 1.0)) ) ) ) )
Test (hit any key to stop):
(pendulum 40 1 36)
Prolog
SWI-Prolog has a graphic interface XPCE.
:- use_module(library(pce)).
pendulum :-
new(D, window('Pendulum')),
send(D, size, size(560, 300)),
new(Line, line(80, 50, 480, 50)),
send(D, display, Line),
new(Circle, circle(20)),
send(Circle, fill_pattern, colour(@default, 0, 0, 0)),
new(Boule, circle(60)),
send(Boule, fill_pattern, colour(@default, 0, 0, 0)),
send(D, display, Circle, point(270,40)),
send(Circle, handle, handle(h/2, w/2, in)),
send(Boule, handle, handle(h/2, w/2, out)),
send(Circle, connect, Boule, link(in, out, line(0,0,0,0,none))),
new(Anim, animation(D, 0.0, Boule, 200.0)),
send(D, done_message, and(message(Anim, free),
message(Boule, free),
message(Circle, free),
message(@receiver,destroy))),
send(Anim?mytimer, start),
send(D, open).
:- pce_begin_class(animation(window, angle, boule, len_pendulum), object).
variable(window, object, both, "Display window").
variable(boule, object, both, "bowl of the pendulum").
variable(len_pendulum, object, both, "len of the pendulum").
variable(angle, object, both, "angle with the horizontal").
variable(delta, object, both, "increment of the angle").
variable(mytimer, timer, both, "timer of the animation").
initialise(P, W:object, A:object, B : object, L:object) :->
"Creation of the object"::
send(P, window, W),
send(P, angle, A),
send(P, boule, B),
send(P, len_pendulum, L),
send(P, delta, 0.01),
send(P, mytimer, new(_, timer(0.01,message(P, anim_message)))).
% method called when the object is destroyed
% first the timer is stopped
% then all the resources are freed
unlink(P) :->
send(P?mytimer, stop),
send(P, send_super, unlink).
% message processed by the timer
anim_message(P) :->
get(P, angle, A),
get(P, len_pendulum, L),
calc(A, L, X, Y),
get(P, window, W),
get(P, boule, B),
send(W, display, B, point(X,Y)),
% computation of the next position
get(P, delta, D),
next_Angle(A, D, NA, ND),
send(P, angle, NA),
send(P, delta, ND).
:- pce_end_class.
% computation of the position of the bowl.
calc(Ang, Len, X, Y) :-
X is Len * cos(Ang)+ 250,
Y is Len * sin(Ang) + 20.
% computation of the next angle
% if we reach 0 or pi, delta change.
next_Angle(A, D, NA, ND) :-
NA is D + A,
(((D > 0, abs(pi-NA) < 0.01); (D < 0, abs(NA) < 0.01))->
ND = - D;
ND = D).
PureBasic
If the code was part of a larger application it could be improved by specifying constants for the locations of image elements.
Procedure handleError(x, msg.s)
If Not x
MessageRequester("Error", msg)
End
EndIf
EndProcedure
#ScreenW = 320
#ScreenH = 210
handleError(OpenWindow(0, 0, 0, #ScreenW, #ScreenH, "Animated Pendulum", #PB_Window_SystemMenu), "Can't open window.")
handleError(InitSprite(), "Can't setup sprite display.")
handleError(OpenWindowedScreen(WindowID(0), 0, 0, #ScreenW, #ScreenH, 0, 0, 0), "Can't open screen.")
Enumeration ;sprites
#bob_spr
#ceiling_spr
#pivot_spr
EndEnumeration
TransparentSpriteColor(#PB_Default, RGB(255, 0, 255))
CreateSprite(#bob_spr, 32, 32)
StartDrawing(SpriteOutput(#bob_spr))
Box(0, 0, 32, 32, RGB(255, 0, 255))
Circle(16, 16, 15, RGB(253, 252, 3))
DrawingMode(#PB_2DDrawing_Outlined)
Circle(16, 16, 15, RGB(0, 0, 0))
StopDrawing()
CreateSprite(#pivot_spr, 10, 10)
StartDrawing(SpriteOutput(#pivot_spr))
Box(0, 0, 10, 10, RGB(255, 0, 255))
Circle(5, 5, 4, RGB(125, 125, 125))
DrawingMode(#PB_2DDrawing_Outlined)
Circle(5, 5, 4, RGB(0,0 , 0))
StopDrawing()
CreateSprite(#ceiling_spr,#ScreenW,2)
StartDrawing(SpriteOutput(#ceiling_spr))
Box(0,0,SpriteWidth(#ceiling_spr), SpriteHeight(#ceiling_spr), RGB(126, 126, 126))
StopDrawing()
Structure pendulum
length.d ; meters
constant.d ; -g/l
gravity.d ; m/s²
angle.d ; radians
velocity.d ; m/s
EndStructure
Procedure initPendulum(*pendulum.pendulum, length.d = 1.0, gravity.d = 9.81, initialAngle.d = #PI / 2)
With *pendulum
\length = length
\gravity = gravity
\angle = initialAngle
\constant = -gravity / length
\velocity = 0.0
EndWith
EndProcedure
Procedure updatePendulum(*pendulum.pendulum, deltaTime.d)
deltaTime = deltaTime / 1000.0 ;ms
Protected acceleration.d = *pendulum\constant * Sin(*pendulum\angle)
*pendulum\velocity + acceleration * deltaTime
*pendulum\angle + *pendulum\velocity * deltaTime
EndProcedure
Procedure drawBackground()
ClearScreen(RGB(190,190,190))
;draw ceiling
DisplaySprite(#ceiling_spr, 0, 47)
;draw pivot
DisplayTransparentSprite(#pivot_spr, 154,43) ;origin in upper-left
EndProcedure
Procedure drawPendulum(*pendulum.pendulum)
;draw rod
Protected x = *pendulum\length * 140 * Sin(*pendulum\angle) ;scale = 1 m/140 pixels
Protected y = *pendulum\length * 140 * Cos(*pendulum\angle)
StartDrawing(ScreenOutput())
LineXY(154 + 5,43 + 5, 154 + 5 + x, 43 + 5 + y) ;draw from pivot-center to bob-center, adjusting for origins
StopDrawing()
;draw bob
DisplayTransparentSprite(#bob_spr, 154 + 5 - 16 + x, 43 + 5 - 16 + y) ;adj for origin in upper-left
EndProcedure
Define pendulum.pendulum, event
initPendulum(pendulum)
drawPendulum(pendulum)
AddWindowTimer(0, 1, 50)
Repeat
event = WindowEvent()
Select event
Case #pb_event_timer
drawBackground()
Select EventTimer()
Case 1
updatePendulum(pendulum, 50)
drawPendulum(pendulum)
EndSelect
FlipBuffers()
Case #PB_Event_CloseWindow
Break
EndSelect
ForEver
Python
==={{libheader|pygame}}===
{{trans|C}}
import pygame, sys from pygame.locals import * from math import sin, cos, radians pygame.init() WINDOWSIZE = 250 TIMETICK = 100 BOBSIZE = 15 window = pygame.display.set_mode((WINDOWSIZE, WINDOWSIZE)) pygame.display.set_caption("Pendulum") screen = pygame.display.get_surface() screen.fill((255,255,255)) PIVOT = (WINDOWSIZE/2, WINDOWSIZE/10) SWINGLENGTH = PIVOT[1]*4 class BobMass(pygame.sprite.Sprite): def __init__(self): pygame.sprite.Sprite.__init__(self) self.theta = 45 self.dtheta = 0 self.rect = pygame.Rect(PIVOT[0]-SWINGLENGTH*cos(radians(self.theta)), PIVOT[1]+SWINGLENGTH*sin(radians(self.theta)), 1,1) self.draw() def recomputeAngle(self): scaling = 3000.0/(SWINGLENGTH**2) firstDDtheta = -sin(radians(self.theta))*scaling midDtheta = self.dtheta + firstDDtheta midtheta = self.theta + (self.dtheta + midDtheta)/2.0 midDDtheta = -sin(radians(midtheta))*scaling midDtheta = self.dtheta + (firstDDtheta + midDDtheta)/2 midtheta = self.theta + (self.dtheta + midDtheta)/2 midDDtheta = -sin(radians(midtheta)) * scaling lastDtheta = midDtheta + midDDtheta lasttheta = midtheta + (midDtheta + lastDtheta)/2.0 lastDDtheta = -sin(radians(lasttheta)) * scaling lastDtheta = midDtheta + (midDDtheta + lastDDtheta)/2.0 lasttheta = midtheta + (midDtheta + lastDtheta)/2.0 self.dtheta = lastDtheta self.theta = lasttheta self.rect = pygame.Rect(PIVOT[0]- SWINGLENGTH*sin(radians(self.theta)), PIVOT[1]+ SWINGLENGTH*cos(radians(self.theta)),1,1) def draw(self): pygame.draw.circle(screen, (0,0,0), PIVOT, 5, 0) pygame.draw.circle(screen, (0,0,0), self.rect.center, BOBSIZE, 0) pygame.draw.aaline(screen, (0,0,0), PIVOT, self.rect.center) pygame.draw.line(screen, (0,0,0), (0, PIVOT[1]), (WINDOWSIZE, PIVOT[1])) def update(self): self.recomputeAngle() screen.fill((255,255,255)) self.draw() bob = BobMass() TICK = USEREVENT + 2 pygame.time.set_timer(TICK, TIMETICK) def input(events): for event in events: if event.type == QUIT: sys.exit(0) elif event.type == TICK: bob.update() while True: input(pygame.event.get()) pygame.display.flip()
Racket
#lang racket
(require 2htdp/image 2htdp/universe)
(define (pendulum)
(define (accel θ) (- (sin θ)))
(define θ (/ pi 2.5))
(define θ′ 0)
(define θ′′ (accel (/ pi 2.5)))
(define (x θ) (+ 200 (* 150 (sin θ))))
(define (y θ) (* 150 (cos θ)))
(λ (n)
(define p-image (underlay/xy (add-line (empty-scene 400 200) 200 0 (x θ) (y θ) "black")
(- (x θ) 5) (- (y θ) 5) (circle 5 "solid" "blue")))
(set! θ (+ θ (* θ′ 0.04)))
(set! θ′ (+ θ′ (* (accel θ) 0.04)))
p-image))
(animate (pendulum))
Ring
# Project : Animate a pendulum
load "guilib.ring"
load "stdlib.ring"
CounterMan = 1
paint = null
pi = 22/7
theta = pi/180*40
g = 9.81
l = 0.50
speed = 0
new qapp
{
win1 = new qwidget() {
setwindowtitle("Animate a pendulum")
setgeometry(100,100,800,600)
label1 = new qlabel(win1) {
setgeometry(10,10,800,600)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,500,100,30)
settext("draw")
setclickevent("draw()")
}
TimerMan = new qtimer(win1)
{
setinterval(1000)
settimeoutevent("draw()")
start()
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
paint = new qpainter() {
begin(p1)
setpen(pen)
ptime()
endpaint()
}
label1 { setpicture(p1) show() }
return
func ptime()
TimerMan.start()
pPlaySleep()
sleep(0.1)
CounterMan++
if CounterMan = 20
TimerMan.stop()
ok
func pPlaySleep()
pendulum(theta, l)
pendulum(theta, l)
accel = - g * sin(theta) / l / 100
speed = speed + accel / 100
theta = theta + speed
func pendulum(a, l)
pivotx = 640
pivoty = 800
bobx = pivotx + l * 1000 * sin(a)
boby = pivoty - l * 1000 * cos(a)
paint.drawline(pivotx, pivoty, bobx, boby)
paint.drawellipse(bobx + 24 * sin(a), boby - 24 * cos(a), 24, 24)
Output video: [https://www.dropbox.com/s/j9usrmmdy9pajmp/CalmoSoftPendulum.avi?dl=0 Animate a pendulum]
RLaB
The plane pendulum motion is an interesting and easy problem in which the facilities of RLaB for numerical computation and simulation are easily accessible. The parameters of the problem are , the length of the arm, and the magnitude of the gravity.
We start with the mathematical transliteration of the problem. We solve it in plane (2-D) in terms of describing the angle between the -axis and the arm of the pendulum, where the downwards direction is taken as positive. The Newton equation of motion, which is a second-order non-linear ordinary differential equation (ODE) reads : In our example, we will solve the problem as, so called, initial value problem (IVP). That is, we will specify that at the time ''t=0'' the pendulum was at rest , extended at an angle radians (equivalent to 30 degrees).
RLaB has the facilities to solve ODE IVP which are accessible through ''odeiv'' solver. This solver requires that the ODE be written as the first order differential equation, : Here, we introduced a vector , for which the original ODE reads : :. The RLaB script that solves the problem is
//
// example: solve ODE for pendulum
//
// we first define the first derivative function for the solver
dudt = function(t, u, p)
{
// t-> time
// u->[theta, dtheta/dt ]
// p-> g/L, parameter
rval = zeros(2,1);
rval[1] = u[2];
rval[2] = -p[1] * sin(u[1]);
return rval;
};
// now we solve the problem
// physical parameters
L = 5; // (m), the length of the arm of the pendulum
p = mks.g / L; // RLaB has a built-in list 'mks' which contains large number of physical constants and conversion factors
T0 = 2*const.pi*sqrt(L/mks.g); // approximate period of the pendulum
// initial conditions
theta0 = 30; // degrees, initial angle of deflection of pendulum
u0 = [theta0*const.pi/180, 0]; // RLaB has a built-in list 'const' of mathematical constants.
// times at which we want solution
t = [0:4:1/64] * T0; // solve for 4 approximate periods with at time points spaced at T0/64
// prepare ODEIV solver
optsode = <<>>;
optsode.eabs = 1e-6; // relative error for step size
optsode.erel = 1e-6; // absolute error for step size
optsode.delta_t = 1e-6; // maximum dt that code is allowed
optsode.stdout = stderr(); // open the text console and in it print the results of each step of calculation
optsode.imethod = 5; // use method No. 5 from the odeiv toolkit, Runge-Kutta 8th order Prince-Dormand method
//optsode.phase_space = 0; // the solver returns [t, u1(t), u2(t)] which is default behavior
optsode.phase_space = 1; // the solver returns [t, u1(t), u2(t), d(u1)/dt(t), d(u2)/dt]
// solver do my bidding
y = odeiv(dudt, p, t, u0, optsode);
// Make an animation. We choose to use 'pgplot' rather then 'gnuplot' interface because the former is
// faster and thus less cache-demanding, while the latter can be very cache-demanding (it may slow your
// linux system quite down if one sends lots of plots for gnuplot to plot).
plwins (1); // we will use one pgplot-window
plwin(1); // plot to pgplot-window No. 1; necessary if using more than one pgplot window
plimits (-L,L, -1.25*L, 0.25*L);
xlabel ("x-coordinate");
ylabel ("z-coordinate");
plegend ("Arm");
for (i in 1:y.nr)
{
// plot a line between the pivot point at (0,0) and the current position of the pendulum
arm_line = [0,0; L*sin(y[i;2]), -L*cos(y[i;2])]; // this is because theta is between the arm and the z-coordinate
plot (arm_line);
sleep (0.1); // sleep 0.1 seconds between plots
}
Ruby
==={{libheader|Ruby/Tk}}===
{{trans|Tcl}} This does not have the window resizing handling that Tcl does -- I did not spend enough time in the docs to figure out how to get the new window size out of the configuration event. Of interest when running this pendulum side-by-side with the Tcl one: the Tcl pendulum swings noticibly faster.
require 'tk' $root = TkRoot.new("title" => "Pendulum Animation") $canvas = TkCanvas.new($root) do width 320 height 200 create TkcLine, 0,25,320,25, 'tags' => 'plate', 'width' => 2, 'fill' => 'grey50' create TkcOval, 155,20,165,30, 'tags' => 'pivot', 'outline' => "", 'fill' => 'grey50' create TkcLine, 1,1,1,1, 'tags' => 'rod', 'width' => 3, 'fill' => 'black' create TkcOval, 1,1,2,2, 'tags' => 'bob', 'outline' => 'black', 'fill' => 'yellow' end $canvas.raise('pivot') $canvas.pack('fill' => 'both', 'expand' => true) $Theta = 45.0 $dTheta = 0.0 $length = 150 $homeX = 160 $homeY = 25 def show_pendulum angle = $Theta * Math::PI / 180 x = $homeX + $length * Math.sin(angle) y = $homeY + $length * Math.cos(angle) $canvas.coords('rod', $homeX, $homeY, x, y) $canvas.coords('bob', x-15, y-15, x+15, y+15) end def recompute_angle scaling = 3000.0 / ($length ** 2) # first estimate firstDDTheta = -Math.sin($Theta * Math::PI / 180) * scaling midDTheta = $dTheta + firstDDTheta midTheta = $Theta + ($dTheta + midDTheta)/2 # second estimate midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling midDTheta = $dTheta + (firstDDTheta + midDDTheta)/2 midTheta = $Theta + ($dTheta + midDTheta)/2 # again, first midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling lastDTheta = midDTheta + midDDTheta lastTheta = midTheta + (midDTheta + lastDTheta)/2 # again, second lastDDTheta = -Math.sin(lastTheta * Math::PI/180) * scaling lastDTheta = midDTheta + (midDDTheta + lastDDTheta)/2 lastTheta = midTheta + (midDTheta + lastDTheta)/2 # Now put the values back in our globals $dTheta = lastDTheta $Theta = lastTheta end def animate recompute_angle show_pendulum $after_id = $root.after(15) {animate} end show_pendulum $after_id = $root.after(500) {animate} $canvas.bind('<Destroy>') {$root.after_cancel($after_id)} Tk.mainloop
==={{libheader|Shoes}}===
Shoes.app(:width => 320, :height => 200) do @centerX = 160 @centerY = 25 @length = 150 @diameter = 15 @Theta = 45.0 @dTheta = 0.0 stroke gray strokewidth 3 line 0,25,320,25 oval 155,20,10 stroke black @rod = line(@centerX, @centerY, @centerX, @centerY + @length) @bob = oval(@centerX - @diameter, @centerY + @length - @diameter, 2*@diameter) animate(24) do |i| recompute_angle show_pendulum end def show_pendulum angle = (90 + @Theta) * Math::PI / 180 x = @centerX + (Math.cos(angle) * @length).to_i y = @centerY + (Math.sin(angle) * @length).to_i @rod.remove strokewidth 3 @rod = line(@centerX, @centerY, x, y) @bob.move(x-@diameter, y-@diameter) end def recompute_angle scaling = 3000.0 / (@length **2) # first estimate firstDDTheta = -Math.sin(@Theta * Math::PI / 180) * scaling midDTheta = @dTheta + firstDDTheta midTheta = @Theta + (@dTheta + midDTheta)/2 # second estimate midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling midDTheta = @dTheta + (firstDDTheta + midDDTheta)/2 midTheta = @Theta + (@dTheta + midDTheta)/2 # again, first midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling lastDTheta = midDTheta + midDDTheta lastTheta = midTheta + (midDTheta + lastDTheta)/2 # again, second lastDDTheta = -Math.sin(lastTheta * Math::PI/180) * scaling lastDTheta = midDTheta + (midDDTheta + lastDDTheta)/2 lastTheta = midTheta + (midDTheta + lastDTheta)/2 # Now put the values back in our globals @dTheta = lastDTheta @Theta = lastTheta end end
==={{libheader|Ruby/Gosu}}===
#!/bin/ruby begin; require 'rubygems'; rescue; end require 'gosu' include Gosu # Screen size W = 640 H = 480 # Full-screen mode FS = false # Screen update rate (Hz) FPS = 60 class Pendulum attr_accessor :theta, :friction def initialize( win, x, y, length, radius, bob = true, friction = false) @win = win @centerX = x @centerY = y @length = length @radius = radius @bob = bob @friction = friction @theta = 60.0 @omega = 0.0 @scale = 2.0 / FPS end def draw @win.translate(@centerX, @centerY) { @win.rotate(@theta) { @win.draw_quad(-1, 0, 0x3F_FF_FF_FF, 1, 0, 0x3F_FF_FF_00, 1, @length, 0x3F_FF_FF_00, -1, @length, 0x3F_FF_FF_FF ) if @bob @win.translate(0, @length) { @win.draw_quad(0, -@radius, Color::RED, @radius, 0, Color::BLUE, 0, @radius, Color::WHITE, -@radius, 0, Color::BLUE ) } end } } end def update # Thanks to Hugo Elias for the formula (and explanation thereof) @theta += @omega @omega = @omega - (Math.sin(@theta * Math::PI / 180) / (@length * @scale)) @theta *= 0.999 if @friction end end # Pendulum class class GfxWindow < Window def initialize # Initialize the base class super W, H, FS, 1.0 / FPS * 1000 # self.caption = "You're getting sleeeeepy..." self.caption = "Ruby/Gosu Pendulum Simulator (Space toggles friction)" @n = 1 # Try changing this number! @pendulums = [] (1..@n).each do |i| @pendulums.push Pendulum.new( self, W / 2, H / 10, H * 0.75 * (i / @n.to_f), H / 60 ) end end def draw @pendulums.each { |pen| pen.draw } end def update @pendulums.each { |pen| pen.update } end def button_up(id) if id == KbSpace @pendulums.each { |pen| pen.friction = !pen.friction pen.theta = (pen.theta <=> 0) * 45.0 unless pen.friction } else close end end def needs_cursor?() true end end # GfxWindow class begin GfxWindow.new.show rescue Exception => e puts e.message, e.backtrace gets end
Scala
{{libheader|Scala}}
import java.awt.Color import java.util.concurrent.{Executors, TimeUnit} import scala.swing.{Graphics2D, MainFrame, Panel, SimpleSwingApplication} import scala.swing.Swing.pair2Dimension object Pendulum extends SimpleSwingApplication { val length = 100 lazy val ui = new Panel { import scala.math.{cos, Pi, sin} background = Color.white preferredSize = (2 * length + 50, length / 2 * 3) peer.setDoubleBuffered(true) var angle: Double = Pi / 2 override def paintComponent(g: Graphics2D): Unit = { super.paintComponent(g) val (anchorX, anchorY) = (size.width / 2, size.height / 4) val (ballX, ballY) = (anchorX + (sin(angle) * length).toInt, anchorY + (cos(angle) * length).toInt) g.setColor(Color.lightGray) g.drawLine(anchorX - 2 * length, anchorY, anchorX + 2 * length, anchorY) g.setColor(Color.black) g.drawLine(anchorX, anchorY, ballX, ballY) g.fillOval(anchorX - 3, anchorY - 4, 7, 7) g.drawOval(ballX - 7, ballY - 7, 14, 14) g.setColor(Color.yellow) g.fillOval(ballX - 7, ballY - 7, 14, 14) } val animate: Runnable = new Runnable { var angleVelocity = 0.0 var dt = 0.1 override def run(): Unit = { angleVelocity += -9.81 / length * Math.sin(angle) * dt angle += angleVelocity * dt repaint() } } } override def top = new MainFrame { title = "Rosetta Code >>> Task: Animate a pendulum | Language: Scala" contents = ui centerOnScreen() Executors. newSingleThreadScheduledExecutor(). scheduleAtFixedRate(ui.animate, 0, 15, TimeUnit.MILLISECONDS) } }
Scheme
{{libheader|Scheme/PsTk}}
{{trans|Ruby}}
This is a direct translation of the Ruby/Tk example into Scheme + PS/Tk.
#!r6rs
;;; R6RS implementation of Pendulum Animation
(import (rnrs)
(lib pstk main) ; change this for your pstk installation
)
(define PI 3.14159)
(define *conv-radians* (/ PI 180))
(define *theta* 45.0)
(define *d-theta* 0.0)
(define *length* 150)
(define *home-x* 160)
(define *home-y* 25)
;;; estimates new angle of pendulum
(define (recompute-angle)
(define (avg a b) (/ (+ a b) 2))
(let* ((scaling (/ 3000.0 (* *length* *length*)))
; first estimate
(first-dd-theta (- (* (sin (* *theta* *conv-radians*)) scaling)))
(mid-d-theta (+ *d-theta* first-dd-theta))
(mid-theta (+ *theta* (avg *d-theta* mid-d-theta)))
; second estimate
(mid-dd-theta (- (* (sin (* mid-theta *conv-radians*)) scaling)))
(mid-d-theta-2 (+ *d-theta* (avg first-dd-theta mid-dd-theta)))
(mid-theta-2 (+ *theta* (avg *d-theta* mid-d-theta-2)))
; again first
(mid-dd-theta-2 (- (* (sin (* mid-theta-2 *conv-radians*)) scaling)))
(last-d-theta (+ mid-d-theta-2 mid-dd-theta-2))
(last-theta (+ mid-theta-2 (avg mid-d-theta-2 last-d-theta)))
; again second
(last-dd-theta (- (* (sin (* last-theta *conv-radians*)) scaling)))
(last-d-theta-2 (+ mid-d-theta-2 (avg mid-dd-theta-2 last-dd-theta)))
(last-theta-2 (+ mid-theta-2 (avg mid-d-theta-2 last-d-theta-2))))
; put values back in globals
(set! *d-theta* last-d-theta-2)
(set! *theta* last-theta-2)))
;;; The main event loop and graphics context
(let ((tk (tk-start)))
(tk/wm 'title tk "Pendulum Animation")
(let ((canvas (tk 'create-widget 'canvas)))
;;; redraw the pendulum on canvas
;;; - uses angle and length to compute new (x,y) position of bob
(define (show-pendulum canvas)
(let* ((pendulum-angle (* *conv-radians* *theta*))
(x (+ *home-x* (* *length* (sin pendulum-angle))))
(y (+ *home-y* (* *length* (cos pendulum-angle)))))
(canvas 'coords 'rod *home-x* *home-y* x y)
(canvas 'coords 'bob (- x 15) (- y 15) (+ x 15) (+ y 15))))
;;; move the pendulum and repeat after 20ms
(define (animate)
(recompute-angle)
(show-pendulum canvas)
(tk/after 20 animate))
;; layout the canvas
(tk/grid canvas 'column: 0 'row: 0)
(canvas 'create 'line 0 25 320 25 'tags: 'plate 'width: 2 'fill: 'grey50)
(canvas 'create 'oval 155 20 165 30 'tags: 'pivot 'outline: "" 'fill: 'grey50)
(canvas 'create 'line 1 1 1 1 'tags: 'rod 'width: 3 'fill: 'black)
(canvas 'create 'oval 1 1 2 2 'tags: 'bob 'outline: 'black 'fill: 'yellow)
;; get everything started
(show-pendulum canvas)
(tk/after 500 animate)
(tk-event-loop tk)))
Scilab
The animation is displayed on a graphic window, and won't stop until it shows all positions calculated unless the user abort the execution on Scilab console.
//No. of steps steps=300;
//Setting deltaT or duration (comment either of the lines below) //deltaT=0.1; t_max=t0+deltaT*steps; t_max=5; deltaT=(t_max-t0)/steps;
if t_max<=t0 then error("Check duration (t0 and t_f), number of steps and deltaT."); end
//Initial position not_a_pendulum=%F; t=zeros(1,steps); t(1)=t0; //time theta=zeros(1,steps); theta(1)=theta0; //angle F=zeros(1,steps); F(1)=bob_massgsin(theta0); //force A=zeros(1,steps); A(1)=F(1)/bob_mass; //acceleration V=zeros(1,steps); V(1)=v0; //linear speed W=zeros(1,steps); W(1)=v0/L; //angular speed
for i=2:steps t(i)=t(i-1)+deltaT; V(i)=A(i-1)deltaT+V(i-1); W(i)=V(i)/L; theta(i)=theta(i-1)+W(i)deltaT; F(i)=bob_massgsin(theta(i)); A(i)=F(i)/bob_mass; if (abs(theta(i))>=%pi | (abs(theta(i))==0 & V(i)==0)) & ~not_a_pendulum then disp("Initial conditions do not describe a pendulum."); not_a_pendulum = %T; end end clear i
//Ploting the pendulum bob_r=0.08L; bob_shape=bob_rexp(%i.linspace(0,360,20)/180%pi);
bob_pos=zeros(20,steps); rod_pos=zeros(1,steps); for i=1:steps rod_pos(i)=Lexp(%i(-%pi/2+theta(i))); bob_pos(:,i)=bob_shape'+rod_pos(i); end clear i
scf(0); clf(); xname("Simple gravity pendulum"); plot2d(real([0 rod_pos(1)]),imag([0 rod_pos(1)])); axes=gca(); axes.isoview="on"; axes.children(1).children.mark_style=3; axes.children(1).children.mark_size=1; axes.children(1).children.thickness=3;
plot2d(real(bob_pos(:,1)),imag(bob_pos(:,1))); axes=gca(); axes.children(1).children.fill_mode="on"; axes.children(1).children.foreground=2; axes.children(1).children.background=2;
if max(imag(bob_pos))>0 then axes.data_bounds=[-L-bob_r,-L-1.01bob_r;L+bob_r,max(imag(bob_pos))]; else axes.data_bounds=[-L-bob_r,-L-1.01bob_r;L+bob_r,bob_r]; end
//Animating the plot disp("Duration: "+string(max(t)+deltaT-t0)+"s."); sleep(850); for i=2:steps axes.children(1).children.data=[real(bob_pos(:,i)), imag(bob_pos(:,i))]; axes.children(2).children.data=[0, 0; real(rod_pos(i)), imag(rod_pos(i))]; sleep(deltaT*1000) end clear i
## SequenceL
{{libheader|EaselSL}}
Using the [https://github.com/bethune-bryant/Easel Easel Engine for SequenceL]
```sequencel>import <Utilities/Sequence.sl
;
import <Utilities/Conversion.sl>;
import <Utilities/Math.sl>;
//region Types
Point ::= (x: int(0), y: int(0));
Color ::= (red: int(0), green: int(0), blue: int(0));
Image ::= (kind: char(1), iColor: Color(0), vert1: Point(0), vert2: Point(0), vert3: Point(0), center: Point(0),
radius: int(0), height: int(0), width: int(0), message: char(1), source: char(1));
Click ::= (clicked: bool(0), clPoint: Point(0));
Input ::= (iClick: Click(0), keys: char(1));
//endregion
//region Helpers
### ================================================================
//region Constructor-Functions-------------------------------------------------
point(a(0), b(0)) := (x: a, y: b);
color(r(0), g(0), b(0)) := (red: r, green: g, blue: b);
segment(e1(0), e2(0), c(0)) := (kind: "segment", vert1: e1, vert2: e2, iColor: c);
disc(ce(0), rad(0), c(0)) := (kind: "disc", center: ce, radius: rad, iColor: c);
//endregion----------------------------------------------------------------------
//region Colors----------------------------------------------------------------
dBlack := color(0, 0, 0);
dYellow := color(255, 255, 0);
//endregion----------------------------------------------------------------------
//endregion
### =======================================================================
//
### ==============Easel=Functions==========================================
State ::= (angle: float(0), angleVelocity: float(0), angleAccel: float(0));
initialState := (angle: pi/2, angleVelocity: 0.0, angleAccel: 0.0);
dt := 0.3;
length := 450;
anchor := point(500, 750);
newState(I(0), S(0)) :=
let
newAngle := S.angle + newAngleVelocity * dt;
newAngleVelocity := S.angleVelocity + newAngleAccel * dt;
newAngleAccel := -9.81 / length * sin(S.angle);
in
(angle: newAngle, angleVelocity: newAngleVelocity, angleAccel: newAngleAccel);
sounds(I(0), S(0)) := ["ding"] when I.iClick.clicked else [];
images(S(0)) :=
let
pendulum := pendulumLocation(S.angle);
in
[segment(anchor, pendulum, dBlack),
disc(pendulum, 30, dYellow),
disc(anchor, 5, dBlack)];
pendulumLocation(angle) :=
let
x := anchor.x + round(sin(angle) * length);
y := anchor.y - round(cos(angle) * length);
in
point(x, y);
//
### ==========End=Easel=Functions==========================================
{{out}} [http://i.imgur.com/ZR2sK54.gifv GIF of Output]
Sidef
{{trans|Perl}}
require('Tk') var root = %s<MainWindow>.new('-title' => 'Pendulum Animation') var canvas = root.Canvas('-width' => 320, '-height' => 200) canvas.createLine( 0, 25, 320, 25, '-tags' => <plate>, '-width' => 2, '-fill' => :grey50) canvas.createOval(155, 20, 165, 30, '-tags' => <pivot outline>, '-fill' => :grey50) canvas.createLine( 1, 1, 1, 1, '-tags' => <rod width>, '-width' => 3, '-fill' => :black) canvas.createOval( 1, 1, 2, 2, '-tags' => <bob outline>, '-fill' => :yellow) canvas.raise(:pivot) canvas.pack('-fill' => :both, '-expand' => 1) var(θ = 45, Δθ = 0, length = 150, homeX = 160, homeY = 25) func show_pendulum() { var angle = θ.deg2rad var x = (homeX + length*sin(angle)) var y = (homeY + length*cos(angle)) canvas.coords(:rod, homeX, homeY, x, y) canvas.coords(:bob, x - 15, y - 15, x + 15, y + 15) } func recompute_angle() { var scaling = 3000/(length**2) # first estimate var firstΔΔθ = (-sin(θ.deg2rad) * scaling) var midΔθ = (Δθ + firstΔΔθ) var midθ = ((Δθ + midΔθ)/2 + θ) # second estimate var midΔΔθ = (-sin(midθ.deg2rad) * scaling) midΔθ = ((firstΔΔθ + midΔΔθ)/2 + Δθ) midθ = ((Δθ + midΔθ)/2 + θ) # again, first midΔΔθ = (-sin(midθ.deg2rad) * scaling) var lastΔθ = (midΔθ + midΔΔθ) var lastθ = ((midΔθ + lastΔθ)/2 + midθ) # again, second var lastΔΔθ = (-sin(lastθ.deg2rad) * scaling) lastΔθ = ((midΔΔθ + lastΔΔθ)/2 + midΔθ) lastθ = ((midΔθ + lastΔθ)/2 + midθ) # Now put the values back in our globals Δθ = lastΔθ θ = lastθ } func animate(Ref id) { recompute_angle() show_pendulum() *id = root.after(15 => { animate(id) }) } show_pendulum() var after_id = root.after(500 => { animate(\after_id) }) canvas.bind('<Destroy>' => { after_id.cancel }) %S<Tk>.MainLoop()
smart BASIC
'Pendulum
'By Dutchman
' --- constants
g=9.81 ' accelleration of gravity
l=1 ' length of pendulum
GET SCREEN SIZE sw,sh
pivotx=sw/2
pivoty=150
' --- initialise graphics
GRAPHICS
DRAW COLOR 1,0,0
FILL COLOR 0,0,1
DRAW SIZE 2
' --- initialise pendulum
theta=1 ' initial displacement in radians
speed=0
' --- loop
DO
bobx=pivotx+100*l*SIN(theta)
boby=pivoty-100*l*COS(theta)
GOSUB Plot
PAUSE 0.01
accel=g*SIN(theta)/l/100
speed=speed+accel
theta=theta+speed
UNTIL 0
END
' --- subroutine
Plot:
REFRESH OFF
GRAPHICS CLEAR 1,1,0.5
DRAW LINE pivotx,pivoty TO bobx,boby
FILL CIRCLE bobx,boby SIZE 10
REFRESH ON
RETURN
We hope that the webmaster will soon have image uploads enabled again so that we can show a screen shot.
Tcl
{{works with|Tcl|8.5}} ==={{libheader|Tk}}===
package require Tcl 8.5 package require Tk # Make the graphical entities pack [canvas .c -width 320 -height 200] -fill both -expand 1 .c create line 0 25 320 25 -width 2 -fill grey50 -tags plate .c create line 1 1 1 1 -tags rod -width 3 -fill black .c create oval 1 1 2 2 -tags bob -fill yellow -outline black .c create oval 155 20 165 30 -fill grey50 -outline {} -tags pivot # Set some vars set points {} set Theta 45.0 set dTheta 0.0 set pi 3.1415926535897933 set length 150 set homeX 160 # How to respond to a changing in size of the window proc resized {width} { global homeX .c coords plate 0 25 $width 25 set homeX [expr {$width / 2}] .c coords pivot [expr {$homeX-5}] 20 [expr {$homeX+5}] 30 showPendulum } # How to actually arrange the pendulum, mapping the model to the display proc showPendulum {} { global Theta dTheta pi length homeX set angle [expr {$Theta * $pi/180}] set x [expr {$homeX + $length*sin($angle)}] set y [expr {25 + $length*cos($angle)}] .c coords rod $homeX 25 $x $y .c coords bob [expr {$x-15}] [expr {$y-15}] [expr {$x+15}] [expr {$y+15}] } # The dynamic part of the display proc recomputeAngle {} { global Theta dTheta pi length set scaling [expr {3000.0/$length**2}] # first estimate set firstDDTheta [expr {-sin($Theta * $pi/180)*$scaling}] set midDTheta [expr {$dTheta + $firstDDTheta}] set midTheta [expr {$Theta + ($dTheta + $midDTheta)/2}] # second estimate set midDDTheta [expr {-sin($midTheta * $pi/180)*$scaling}] set midDTheta [expr {$dTheta + ($firstDDTheta + $midDDTheta)/2}] set midTheta [expr {$Theta + ($dTheta + $midDTheta)/2}] # Now we do a double-estimate approach for getting the final value # first estimate set midDDTheta [expr {-sin($midTheta * $pi/180)*$scaling}] set lastDTheta [expr {$midDTheta + $midDDTheta}] set lastTheta [expr {$midTheta + ($midDTheta + $lastDTheta)/2}] # second estimate set lastDDTheta [expr {-sin($lastTheta * $pi/180)*$scaling}] set lastDTheta [expr {$midDTheta + ($midDDTheta + $lastDDTheta)/2}] set lastTheta [expr {$midTheta + ($midDTheta + $lastDTheta)/2}] # Now put the values back in our globals set dTheta $lastDTheta set Theta $lastTheta } # Run the animation by updating the physical model then the display proc animate {} { global animation recomputeAngle showPendulum # Reschedule set animation [after 15 animate] } set animation [after 500 animate]; # Extra initial delay is visually pleasing # Callback to handle resizing of the canvas bind .c <Configure> {resized %w} # Callback to stop the animation cleanly when the GUI goes away bind .c <Destroy> {after cancel $animation}
XPL0
include c:\cxpl\codes; \intrinsic 'code' declarations
proc Ball(X0, Y0, R, C); \Draw a filled circle
int X0, Y0, R, C; \center coordinates, radius, color
int X, Y;
for Y:= -R to R do
for X:= -R to R do
if X*X + Y*Y <= R*R then Point(X+X0, Y+Y0, C);
def L = 2.0, \pendulum arm length (meters)
G = 9.81, \acceleration due to gravity (meters/second^2)
Pi = 3.14,
DT = 1.0/72.0; \delta time = screen refresh rate (seconds)
def X0=640/2, Y0=480/2; \anchor point = center coordinate
real S, V, A, T; \arc length, velocity, acceleration, theta angle
int X, Y; \ball coordinates
[SetVid($101); \set 640x480x8 graphic display mode
T:= Pi*0.75; V:= 0.0; \starting angle and velocity
S:= T*L;
repeat A:= -G*Sin(T);
V:= V + A*DT;
S:= S + V*DT;
T:= S/L;
X:= X0 + fix(L*100.0*Sin(T)); \100 scales to fit screen
Y:= Y0 + fix(L*100.0*Cos(T));
Move(X0, Y0); Line(X, Y, 7); \draw pendulum
Ball(X, Y, 10, $E\yellow\);
while port($3DA) & $08 do []; \wait for vertical retrace to go away
repeat until port($3DA) & $08; \wait for vertical retrace signal
Move(X0, Y0); Line(X, Y, 0); \erase pendulum
Ball(X, Y, 10, 0\black\);
until KeyHit; \keystroke terminates program
SetVid(3); \restore normal text screen
]
Yabasic
clear screen
open window 400, 300
window origin "cc"
rodLen = 160
gravity = 2
damp = .989
TWO_PI = pi * 2
angle = 90 * 0.01745329251 // convert degree to radian
repeat
acceleration = -gravity / rodLen * sin(angle)
angle = angle + velocity : if angle > TWO_PI angle = 0
velocity = velocity + acceleration
velocity = velocity * damp
posX = sin(angle) * rodLen
posY = cos(angle) * rodLen - 70
clear window
text -50, -100, "Press 'q' to quit"
color 250, 0, 250
fill circle 0, -70, 4
line 0, -70, posX, posY
color 250, 100, 20
fill circle posX, posY, 10
until(lower$(inkey$(0.02)) = "q")
exit
ZX Spectrum Basic
{{trans|ERRE}} In a real Spectrum it is too slow. Use the BasinC emulator/editor at maximum speed for realistic animation.
10 OVER 1: CLS
20 LET theta=1
30 LET g=9.81
40 LET l=0.5
50 LET speed=0
100 LET pivotx=120
110 LET pivoty=140
120 LET bobx=pivotx+l*100*SIN (theta)
130 LET boby=pivoty+l*100*COS (theta)
140 GO SUB 1000: PAUSE 1: GO SUB 1000
190 LET accel=g*SIN (theta)/l/100
200 LET speed=speed+accel/100
210 LET theta=theta+speed
220 GO TO 100
1000 PLOT pivotx,pivoty: DRAW bobx-pivotx,boby-pivoty
1010 CIRCLE bobx,boby,3
1020 RETURN
{{omit from|LFE}} {{omit from|Maxima}} {{omit from|PARI/GP}} {{omit from|PHP}} {{omit from|SQL PL|It does not handle GUI}}
[[Category:Animation]]