Particle Dynamics

John R. Williams and Abel Sanchez

Newton's Equations

Newton's Equations

Newton's Equations

Newton's Equations

Newton's Equations

Newton's Equations

Newton's Equations

In class Assignment 1.
Here is code starter code to create masses and springs. We'll start with just two masses and one spring to test the code.

<!DOCTYPE html>
<html>
<head>
<script src = 'Vector2D.js'></script>
<script>
var canvas;
var context;
var stiffness = 1;
var mass    = 1;
var deltaT  = 0.1;
var gravity = -1;
var velx, vely;
var trackerFlag =0;
var particles=[];
var springs = [];

window.onload=getCanvas;
function getCanvas(){
  canvas = document.getElementById("myCanvas");
  context =  canvas.getContext ('2d');
}

plotAll();

}
function plotAll(){
	if(!trackerFlag){
		context.clearRect(0, 0, 600, 600);
		var s;
		for(var i=0;i<springs.length;i++){
			s = springs[i];
			DrawLine(s.masses[0].center,s.masses[1].center);
		}
	}
	var radius = mass * 10;
	for(i=0;i<particles.length;i++)DrawCircle(particles[i].center,radius);
}
function TrackerOn(){
	if(trackerFlag===0)
		trackerFlag = 1;  // don't draw the line but track the circle path
	else {
		trackerFlag = 0;
	}
}
	// a spring has particles (masses)
	// it updates itself under gravity
function Spring(p0,p1,stiffness,velocity){
	var masses = [p0,p1];
	var originalLength = p1.center.minus(p0.center).abs();
	
	var updateSpringForces = function updateSpringForces(){
		var c0 = masses[0].center;
		var c1 = masses[1].center;
		var len1 = c1.minus(c0).abs();
		var forcemag = (len1 - originalLength)*stiffness;
		var unitVec = c1.minus(c0).unit();

var f = unitVec.scale(forcemag);
		masses[0].force = masses[0].force.plus(f);
		masses[1].force = masses[1].force.minus(f);
		};

return {masses:masses, originalLength:originalLength,
    updateSpringForces:updateSpringForces};
}
function checkWallCollision(){
  for(var i=0;i<particles.length;i++){
    var m = particles[i];
    var v = m.velocity.x;
    var dx = m.velocity.x * deltaT;
    var dy = m.velocity.y * deltaT;

if (m.center.x + dx > canvas.width || m.center.x + dx < 0){
      m.velocity.x = -m.velocity.x;
    }
    if (m.center.y + dy >= canvas.height || m.center.y + dy <= 0){
      m.velocity.y = -m.velocity.y;
    }
  }
}
// this assumes we have a spring with an original Length and stiffness
function Particle(center,radius){
	var velocity = Vector(0,0);
	var force = Vector(0,0);
	var mass = 1;
  return {center:center, radius:radius,mass:mass,velocity:velocity,
			force:force};
}
function updateDisplacement(p)
{
  p.velocity.x += p.force.x*(deltaT/p.mass);
  p.velocity.y += (p.force.y - gravity*mass)*(deltaT/p.mass);
  //console.log('fx,fy ='+m.force.x+', '+m.force.y +' v ='+m.velocity.x+', '+m.velocity.y);

// check if either mass will hit the wall
  checkWallCollision(p);

// update the position of the masses and draw
  p.center.x += p.velocity.x *deltaT;
  p.center.y += p.velocity.y *deltaT;
  DrawCircle(p.center,5);
}
// on mouse up call this

</body>
</html>

Create two particles. Drag the fixed one so that you get the other to oscillate and create at least two different patters for the orbits. Hand in your screen shots.

Assignment 2
Change the code so that 3 particles are tied together by 2 springs. Hand in a screen shot of the two particles oscillating about the fixed one.

Assignment 3 - Fracture of Materials
If the force in any of the springs exceeds 20 then remove that spring. ie the particles break apart. Make at least 3 groups of 3 particles per group and hand in a screen shot after two of the groups break apart. Hint: Find the code where the spring force is generated. Flag the spring if its greater than 20 (use setDeleteSpring = 'this' to grab a reference to the spring object.) Now after the loop over all springs use var k = springs.indexOf(setDeleteSpring) and then delete the spring from 'springs' by using 'splice'

Particle Dynamics

Newton's Equations

Newton's Equations

Newton's Equations

Newton's Equations

Newton's Equations

Newton's Equations

Newton's Equations

THE END