Hello everyone,
I’ve been working on a simulation of a magnetic pendulum (Magnetic Pendulum for reference). Now, I have a question concerning how you calculate the forces/acceleration:
In examples you find online of the magnetic pendulum (such as the one provided above), and other physics force and acceleration calculations, the forces are calculated at a starting position, the position updated according to time-step dt and then new forces at time t+dt calculated to get a new position and so on. Basic numerical integration, makes sense.
However, I noticed, that if I calculate the forces this way, things don’t go as one would expect. For example: when the pendulum is attracted by a magnet it just stops at the particluar magnet even tough you would expect it to “overswing” a bit. Therefore, I introduced three variables for each force which is all previous forces added together, and now it somehow seems to work correctly.
I’m wondering if
- the way of calculating the forces I used makes sense in a physics simulation and
- if not, then what am I doing wrong? Because it seems to work for other people.
Here’s my code:
sketch.js
p5.disableFriendlyErrors = true;
let magnete = [];
let particles = [];
var maganzahl = 3; //number of magnets
var magradius = 100; //radius of magnets from mid-point
var G = 0.002; //coefficient of force towards middle (gravity)
var R = 0.2; //friction coefficient
var h = 50; //height of bob over magnets
var M = 150000; //strength of magnets
var m = 1; //mass (might not work)
var dt = 0.25; //timestep
var d = 2; //pixel density
var counter2 = 0;
var Reset;
var end = false;
//--------------------------------------------
function setup() {
createCanvas(600, 600);
pixelDensity(d);
background(60);
Reset = createButton('Reset');
Reset.position(width + 19, 49);
Reset.mousePressed(resetcanvas);
//construction of magnets
for (var i = 0; i < maganzahl; i++) {
magnete.push(new Magnet((width / 2) + magradius * cos(TWO_PI * (i / maganzahl)), (height / 2) + magradius * sin(TWO_PI * (i / maganzahl)), i));
}
}
//construction of a new "starting position" by mouse-click
function mousePressed() {
if (mouseX < width && mouseY < height) {
particles.push(new Particle(mouseX, mouseY));
}
}
function draw() {
for (var i = 0; i < particles.length; i++) {
if (particles[i].counter < 1000) {
//5 updates per frame(to speed it up)
for (var k = 0; k < 5; k++) {
for (var j = 0; j < magnete.length; j++) {
particles[i].attracted(magnete[j]);
}
particles[i].update();
particles[i].show2();
}
} else if (particles[i].counter < 1001) {
particles[i].counter += 1;
var nearest = [];
for (var j = 0; j < magnete.length; j++) {
nearest.push(particles[i].near(magnete[j]));
}
if (nearest.indexOf(min(nearest)) == 0) {
var c = color("green");
}
if (nearest.indexOf(min(nearest)) == 1) {
var c = color("purple");
}
if (nearest.indexOf(min(nearest)) == 2) {
var c = color("orange");
}
if (nearest.indexOf(min(nearest)) == 3) {
var c = color("blue");
}
if (nearest.indexOf(min(nearest)) == 4) {
var c = color("red");
}
if (nearest.indexOf(min(nearest)) == 5) {
var c = color("yellow");
}
//show particle trace according to nearest magnet
particles[i].show(c);
}
}
//displaying magnets
for (var i = 0; i < magnete.length; i++) {
magnete[i].show();
}
//displaying mid-point
stroke(255);
circle(width / 2, height / 2, 3);
}
function resetcanvas() {
background(60);
}p5.disableFriendlyErrors = true;
let magnete = [];
let particles = [];
var maganzahl = 3; //number of magnets
var magradius = 100; //radius of magnets from mid-point
var G = 0.002; //coefficient of force towards middle (gravity)
var R = 0.2; //friction coefficient
var h = 50; //height of bob over magnets
var M = 150000; //strength of magnets
var m = 1; //mass (might not work)
var dt = 0.25; //timestep
var d = 2; //pixel density
var counter2 = 0;
var Reset;
var end = false;
//--------------------------------------------
function setup() {
createCanvas(600, 600);
pixelDensity(d);
background(60);
Reset = createButton('Reset');
Reset.position(width + 19, 49);
Reset.mousePressed(resetcanvas);
//construction of magnets
for (var i = 0; i < maganzahl; i++) {
magnete.push(new Magnet((width / 2) + magradius * cos(TWO_PI * (i / maganzahl)), (height / 2) + magradius * sin(TWO_PI * (i / maganzahl)), i));
}
}
//construction of a new "starting position" by mouse-click
function mousePressed() {
if (mouseX < width && mouseY < height) {
particles.push(new Particle(mouseX, mouseY));
}
}
function draw() {
for (var i = 0; i < particles.length; i++) {
if (particles[i].counter < 1000) {
//5 updates per frame(to speed it up)
for (var k = 0; k < 5; k++) {
for (var j = 0; j < magnete.length; j++) {
particles[i].attracted(magnete[j]);
}
particles[i].update();
particles[i].show2();
}
} else if (particles[i].counter < 1001) {
particles[i].counter += 1;
var nearest = [];
for (var j = 0; j < magnete.length; j++) {
nearest.push(particles[i].near(magnete[j]));
}
if (nearest.indexOf(min(nearest)) == 0) {
var c = color("green");
}
if (nearest.indexOf(min(nearest)) == 1) {
var c = color("purple");
}
if (nearest.indexOf(min(nearest)) == 2) {
var c = color("orange");
}
if (nearest.indexOf(min(nearest)) == 3) {
var c = color("blue");
}
if (nearest.indexOf(min(nearest)) == 4) {
var c = color("red");
}
if (nearest.indexOf(min(nearest)) == 5) {
var c = color("yellow");
}
//show particle trace according to nearest magnet
particles[i].show(c);
}
}
//displaying magnets
for (var i = 0; i < magnete.length; i++) {
magnete[i].show();
}
//displaying mid-point
stroke(255);
circle(width / 2, height / 2, 3);
}
function resetcanvas() {
background(60);
}
particles.js
function Particle(x, y) {
this.orgpos = createVector(x, y);
this.pos = createVector(x, y);
this.prev = createVector(x, y);
this.vel = createVector();
this.acc = createVector();
this.accpre = createVector();
this.accprepre = createVector();
this.velprediction = this.vel;
this.magnetf = createVector();
this.gravity = createVector();
this.friction = createVector();
this.shape = new Array();
this.counter = 0;
//calculating new positions
this.update = function() {
//predictor for velocity -> Beeman's algorithm
this.velprediction.add(this.accpre.mult(3 / 2 * dt).add(this.accprepre.mult(-1 / 2 * dt)));
var momgrav = createVector(width / 2 - this.pos.x, height / 2 - this.pos.y);
var momfric = createVector(this.velprediction.x, this.velprediction.y);
momgrav.mult(G * m); //force due to gravity
momfric.mult(-R); //force due to friction
this.gravity.add(momgrav);
this.friction.add(momfric);
//a = F/m
this.acc = createVector((this.magnetf.x + this.gravity.x + this.friction.x) / m, (this.magnetf.y + this.gravity.y + this.friction.y) / m);
//-=Beeman's Algorithm=-
this.vel.add(this.acc.mult(dt * 1 / 3).add(this.accpre.mult(dt * 5 / 6)).add(this.accprepre.mult(-1 / 6 * dt)));
this.pos.add(this.vel.mult(dt).add(this.accpre.mult(dt * dt * 2 / 3)).add(this.accprepre.mult(-1 / 6 * dt * dt)));
this.accprepre = createVector(this.accpre.x, this.accpre.y);
this.accpre = createVector(this.acc.x, this.acc.y);
this.velprediction = createVector(this.vel.x, this.vel.y);
this.counter += 1;
this.shape.push(new p5.Vector(this.pos.x, this.pos.y));
}
//calculating force due to magnets -> attracted called earlier than update in sketch.js
this.attracted = function(target) {
var magn = createVector(target.pos.x - this.pos.x, target.pos.y - this.pos.y);
var dist = sqrt(sq(h) + sq(magn.x) + sq(magn.y)); //distance bob - magnet
strength = M / (Math.pow(dist, 3));
magn.mult(strength);
this.magnetf.add(magn);
}
//calculating distance to target
this.near = function(target) {
var dist = sqrt(sq(h) + sq(this.pos.x - target.pos.x) + sq(this.pos.y - target.pos.y));
return (dist);
}
//trace
this.show = function(col) {
beginShape();
stroke(col);
for (var i = 0; i < this.shape.length - 1; i++) {
line(this.shape[i].x, this.shape[i].y, this.shape[i + 1].x, this.shape[i + 1].y);
strokeWeight(2);
noFill();
}
endShape();
}
//dots
this.show2 = function() {
strokeWeight(1)
point(this.pos.x, this.pos.y);
}
}
magnete.js
function Magnet(x, y, n) {
this.pos = createVector(x, y);
this.n = n;
this.show = function() {
noStroke();
//color for each magnet
if (n == 0) {
fill("green");
}
if (n == 1) {
fill("purple");
}
if (n == 2) {
fill("orange");
}
if (n == 3) {
fill("blue");
}
if (n == 4) {
fill("red");
}
if (n == 5) {
fill("yellow");
}
strokeWeight(4);
circle(this.pos.x, this.pos.y, 10);
}
}
Any help would be greatly appreciated!