// https://thecodingtrain.com/CodingChallenges/093-double-pendulum.html

// https://youtu.be/uWzPe_S-RVE

​

let r1 = 75;

let r2 = 75;

let m1 = 10;

let m2 = 10

let a1 = 0;

let a2 = 0;

let a1_v = 0;

let a2_v = 0;

let g = 0.25;

​

let cx, cy;

let buffer;

​

let timesteps = 1000;

let init_variance = 0.001

​

let x2_past = -1;

let y2_past = -1;

​

function setup() {

  createCanvas(600, 350);

  //Issue with wrong rendering on a retina Mac. See issue: https://github.com/CodingTrain/website/issues/574

  randomSeed(millis()*10000);

  let eps = (random()-0.5)*init_variance;

  pixelDensity(1);

  a1 = PI;

  a2 = PI + eps;

  cx = width / 2;

  cy = height / 2;

  buffer = createGraphics(width, height);

  buffer.background(250);

  buffer.translate(cx, cy);

}

​

function draw() {

  background(250);

  imageMode(CORNER);

  image(buffer, 0, 0, width, height);

  let num1;

  let num2;

  let num3;

  let num4;

  let den;

  let a1_a;

  let a2_a;

  let x1;

  let y1;

​

  let x2;

  let y2;

  for(let t=0; t < timesteps; t++) {

    num1 = -g * (2 * m1 + m2) * sin(a1);

    num2 = -m2 * g * sin(a1 - 2 * a2);

    num3 = -2 * sin(a1 - a2) * m2;

    num4 = a2_v * a2_v * r2 + a1_v * a1_v * r1 * cos(a1 - a2);

    den = r1 * (2 * m1 + m2 - m2 * cos(2 * a1 - 2 * a2));

    a1_a = (num1 + num2 + num3 * num4) / den;

    a1_a /= timesteps;

    num1 = 2 * sin(a1 - a2);

    num2 = (a1_v * a1_v * r1 * (m1 + m2));

    num3 = g * (m1 + m2) * cos(a1);

    num4 = a2_v * a2_v * r2 * m2 * cos(a1 - a2);

    den = r2 * (2 * m1 + m2 - m2 * cos(2 * a1 - 2 * a2));

    a2_a = (num1 * (num2 + num3 + num4)) / den;

    a2_a /= timesteps;

​

​

    x1 = r1 * sin(a1);

    y1 = r1 * cos(a1);

​

    x2 = x1 + r2 * sin(a2);

    y2 = y1 + r2 * cos(a2);

​

    a1_v += a1_a;

    a2_v += a2_a;

    a1 += a1_v/timesteps;

    a2 += a2_v/timesteps;

  }

​

​

  translate(cx, cy);

  stroke(0);

  strokeWeight(0.1);

​

  strokeWeight(1);

  line(0, 0, x1, y1);

  fill(0);

  ellipse(x1, y1, m1*0.2, m1*0.2);

​

  line(x1, y1, x2, y2);

  fill(0);

  ellipse(x2, y2, m2*0.2, m2*0.2);

​

  buffer.stroke(0);

  if (frameCount > 1) {

    stroke(0, 100)

    strokeWeight(0.5);

    buffer.line(x2_past, y2_past, x2, y2);

  }

​

  x2_past = x2;

  y2_past = y2;

}