// 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)))) ); } } }