forked from: forked from: Double Pendulum Symplectic Euler
/**
* Copyright Dokin ( http://wonderfl.net/user/Dokin )
* MIT License ( http://www.opensource.org/licenses/mit-license.php )
* Downloaded from: http://wonderfl.net/c/8dfb
*/
// forked from makc3d's forked from: Double Pendulum Symplectic Euler
// forked from aont's Double Pendulum
package {
import flash.display.Bitmap;
import flash.display.BitmapData;
import flash.display.Sprite;
import flash.events.MouseEvent;
import flash.events.TimerEvent;
import flash.geom.ColorTransform;
import flash.geom.Matrix;
import flash.geom.Point;
import flash.utils.Timer;
[SWF(backgroundColor=0)]
public class DoublePendulum extends Sprite
{
private var line_1:Sprite;
private var line_2:Sprite;
private var circle:Sprite;
private var circleCoords:Array = [];
private var line_ratio:Number;
private var length_1:Number = 0.5;
private var length_2:Number = 0.25;
private var radius:Number = 2;
private var mass_1:Number = 0.05;
private var mass_2:Number = 0.01;
private var color_1:Number = 0x7f0000;
private var color_2:Number = 0xff0000;
private var color_3:Number = 0xff7f00;
private var theta:Number = 0;
private var phi:Number = 0;
private var d_theta:Number = 0;
private var d_phi:Number = 0;
private var center:Number;
private var center_y:Number;
private var dt:Number = 1.0/60;
private var g:Number = 9.8;
private var myTimer:Timer;
private var gamma1:Number = 0;
private var gamma2:Number = 0;
private var friction:Number = 1 - 1e-3;
private var bd:BitmapData;
private var ct:ColorTransform;
public function DoublePendulum()
{
this.parent.addEventListener(MouseEvent.CLICK, MouseClick);
this.center = 230;
this.line_ratio = center / (this.length_1+this.length_2);
line_1 = CreateLine(this.length_1*line_ratio,color_1)
line_2 = CreateLine(this.length_2*line_ratio,color_2);
this.line_1.x = center;
this.line_1.y = center;
bd = new BitmapData (465, 465, true, 0); addChild (new Bitmap (bd));
ct = new ColorTransform; ct.color = color_3;
ct.alphaMultiplier = friction;
circle = new Sprite; circle.graphics.beginFill (0xffffff);
circle.graphics.drawCircle (0, 0, radius); addChild (circle);
this.ReDraw();
this.myTimer = new Timer(this.dt * 1000,0);
this.myTimer.addEventListener(TimerEvent.TIMER,Tick);
this.myTimer.start();
}
private function MouseClick(event:MouseEvent):void
{
theta = Math.atan2(center-event.localY,event.localX-center) + Math.PI /2;
d_theta = 0;
//d_phi = 0;
this.ReDraw();
}
private function ReDraw():void
{
this.line_1.rotation = 90 - this.theta * 180 / Math.PI;
this.line_2.rotation = 90 - this.phi * 180 / Math.PI;
this.line_2.x = center + this.length_1*line_ratio * Math.sin(this.theta) ;
this.line_2.y = center + this.length_1 * line_ratio * Math.cos(this.theta) ;
circle.x = line_2.x + length_2*line_ratio * Math.sin (phi);
circle.y = line_2.y + length_2 * line_ratio * Math.cos (phi);
if (circleCoords.length == 4) circleCoords.shift ();
while (circleCoords.length != 4) circleCoords.push (new Point (circle.x, circle.y));
var m:Matrix = new Matrix, n:Number = 40 / radius;
for (var i:int = 1; i < n + 1; i++) {
var p:Point = spline (circleCoords [0], circleCoords [1], circleCoords [2], circleCoords [3], i / n);
m.tx = p.x; m.ty = p.y;
bd.draw (circle, m);
}
bd.colorTransform (bd.rect, ct);
}
private function CreateLine(length:Number,color:uint):Sprite
{
var line:Sprite = new Sprite();
with(line.graphics)
{
lineStyle(1, color);
moveTo(0,0);
lineTo(length,0);
}
this.addChild(line);
return line;
}
private function Advance():void
{
//var theta_new:Number
//var phi_new:Number;
d_theta += dt*
(
-(mass_1+mass_2)*g*Math.sin(theta)/length_1
+mass_2*g*Math.cos(theta-phi)*Math.sin(phi)/length_1
-mass_2*Math.pow(d_theta,2)*Math.sin(2*(theta-phi))/2
-mass_2*Math.sin(theta-phi)*Math.pow(d_phi,2)*length_2/length_1
) / (mass_1 + mass_2 * Math.pow(Math.sin(theta-phi),2))
-gamma1 * d_theta
;
d_phi += dt*
(
(mass_1+mass_2)*g*Math.cos(theta)*Math.sin(theta-phi)/length_2
+(mass_1+mass_2)*Math.sin(theta-phi)*Math.pow(d_theta,2)*length_1/length_2
+mass_2*Math.pow(d_phi,2)*Math.sin(2*(theta-phi))/2
) / (mass_1 + mass_2 * Math.pow(Math.sin(theta-phi),2))
-gamma2 * d_phi
;
d_theta *= friction;
d_phi *= friction;
theta = ModRadian(theta + d_theta * dt);
phi = ModRadian(phi + d_phi * dt);
}
private function ModRadian(rad:Number):Number
{
while(rad > Math.PI)
{
rad -= 2*Math.PI;
}
while(rad <= -Math.PI)
{
rad += 2*Math.PI;
}
return rad;
}
private function Tick(event:TimerEvent):void
{
this.Advance();
this.ReDraw();
}
/*
* Calculates 2D cubic Catmull-Rom spline.
* @see http://www.mvps.org/directx/articles/catmull/
*/
private function spline (p0:Point, p1:Point, p2:Point, p3:Point, t:Number):Point {
return new Point (
0.5 * (( 2*p1.x) +
t * (( -p0.x +p2.x) +
t * ((2*p0.x -5*p1.x +4*p2.x -p3.x) +
t * ( -p0.x +3*p1.x -3*p2.x +p3.x)))),
0.5 * (( 2*p1.y) +
t * (( -p0.y +p2.y) +
t * ((2*p0.y -5*p1.y +4*p2.y -p3.y) +
t * ( -p0.y +3*p1.y -3*p2.y +p3.y))))
);
}
}
}