I was trying to figure out a way to improve my initial movie that stop and starts the APE engine to allow for the user to drag an object. After mucking around with the original APE classes, I found in Google Groups that there are 2 new classes to allow the use to drag either a CircleParticle or a RectangleParticle.

You can grab the zip file here: http://ape-general.googlegroups.com/web/dragable_particles.zip and here is what can be produced:

package {
    import flash.display.Sprite;
    import flash.events.Event;
	import flash.events.MouseEvent;

    import org.cove.ape.*;

	public class Main extends Sprite {

		private var circle:DragableCircleParticle;
		private var circle2:DragableCircleParticle;

		public function Main()
		{
			init();
		}

		private function init():void
		{
			stage.frameRate = 55;

			// Initialize the engine. The argument here is the time step value.
			// Higher values scale the forces in the sim, making it appear to run
			// faster or slower. Lower values result in more accurate simulations.
			APEngine.init(1/4);

			// set up the default diplay container
			APEngine.container = this;

			APEngine.addMasslessForce(new Vector(0,8));

			var defaultGroup:Group = new Group();

			defaultGroup.collideInternal = true;

            var rect:RectangleParticle = new RectangleParticle(350, 348, 700, 20, 0, true);
            defaultGroup.addParticle(rect);

           	circle = new DragableCircleParticle(350, 150, 25);
			defaultGroup.addParticle(circle);

			circle2 = new DragableCircleParticle(300, 150, 25);
			defaultGroup.addParticle(circle2);

			APEngine.addGroup(defaultGroup);

			addEventListener(Event.ENTER_FRAME, run);
		}

		private function run(e:Event):void
		{
			APEngine.step();
			APEngine.paint();
		}
	}
}

Here is the new class file located in org/cove/ape/DragableCircleParticle.as (relative to my Main.as file)

package org.cove.ape{
	import flash.events.MouseEvent;
	import org.cove.ape.*;
	public class DragableCircleParticle extends CircleParticle{
		private var mouseIsDown:Boolean;
		public function DragableCircleParticle(
				x:Number,
				y:Number,
				radius:Number,
				fixed:Boolean = false,
				mass:Number = 1,
				elasticity:Number = 0.3,
				friction:Number = 0){
			super(x, y, radius, fixed, mass, elasticity, friction);
			alwaysRepaint = fixed;
			mouseIsDown = false;
			sprite.addEventListener(MouseEvent.MOUSE_DOWN,mouseDownHandler);
			sprite.stage.addEventListener(MouseEvent.MOUSE_UP,mouseUpHandler);
			sprite.stage.addEventListener(MouseEvent.MOUSE_MOVE,mouseMoveHandler);
		}
		private function mouseDownHandler(evt:MouseEvent):void{
			mouseIsDown = true;					// on mouse down set mouseIsDown to true
			curr.setTo(evt.stageX,evt.stageY);	// set the current position of the particle to the position of the mouse
			prev.setTo(evt.stageX,evt.stageY);	// set the previous position of the particle to the position of the mouse
		}
		private function mouseUpHandler(evt:MouseEvent):void{
			mouseIsDown = false;			// on mouse up set mouseIsDown to false
		}
		private function mouseMoveHandler(evt:MouseEvent):void{
			if(mouseIsDown){				// On mouse move if the mouse is down
				prev.copy(curr);			// set the previous position to the curent position of the particle
				curr.setTo(evt.stageX,evt.stageY);	// set the current position to the position of the mouse
			}
		}
		public override function update(dt2:Number):void {
			if(!mouseIsDown){		// Don't update if the mouse is down
				super.update(dt2);
			}
		}
	}
}