Double Pendulum Euler

by aont 18 Feb 2010

• Related works: 11

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Physics
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/**
 * Copyright aont ( http://wonderfl.net/user/aont )
 * MIT License ( http://www.opensource.org/licenses/mit-license.php )
 * Downloaded from: http://wonderfl.net/c/lvvN
 */

package {
	import flash.display.Sprite;
	import flash.events.MouseEvent;
	import flash.events.TimerEvent;
	import flash.utils.Timer;
    
	public class DoublePendulum extends Sprite
	{
		private var line_1:Sprite;
		private var line_2:Sprite;
		private var line_ratio:Number;
		private var length_1:Number = 0.5;
		private var length_2:Number = 0.25;
		
		private var mass_1:Number = 0.05;
		private var mass_2:Number = 0.01;
		
		private var color_1:Number = 0xff0000;
		private var color_2:Number = 0x0000ff;
		
		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 = 0.0005;
		private var gamma2:Number = 0.001;
		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;
			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) ;
		}
		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;
			
			theta_new = theta + d_theta * dt;
			phi_new = phi + d_phi * dt;
			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
				;
			
			theta = ModifyRadian(theta_new);
			phi = ModifyRadian(phi_new);			
		} 
		private function ModifyRadian(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();
		}
	}
}