Double Pendulum Simulator

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Overview

In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is chaotic.

Several variants of the double pendulum may be considered; the two limbs may be of equal or unequal lengths and masses, they may be simple pendulums or compound pendulums.

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Functionality

• Users are able to define the mass of each pendulum.
• Users can define the length of each limb.
• Users can also see the motion of the double compound pendulum.

Technologies

This project will be implemented with the following technologies:

• HTML5 Canvas for DOM rendering
• p5.js for drawing functionality

Formula Implementation and mass tracking

Although implementing the original formula is fairly straight forward, it is not as easy to track the locations of balls at all times.

angle1Acc = (-g * (2 * mass1 + mass2) * sin(angle1) + -mass2 * g * sin(angle1 - 2 * angle2) + -2 * sin(angle1 - angle2) * mass2 * angle2Vel * angle2Vel * limb2 + angle1Vel * angle1Vel * limb1 * cos(angle1 - angle2)) / (limb1 * (2 * mass1 + mass2 - mass2 * cos(2 * angle1 - 2 * angle2)));

angle2Acc = (2 * sin(angle1 - angle2) * (angle1Vel * angle1Vel * limb1 * (mass1 + mass2) + g * (mass1 + mass2) * cos(angle1) + angle2Vel * angle2Vel * limb2 * mass2 * cos(angle1 - angle2))) / (limb2 * (2 * mass1 + mass2 - mass2 * cos(2 * angle1 - 2 * angle2)));

The locations of balls are needed at all times because velocity, acceleration, and angle of force are recalculated constantly.

function calculateBallLocations() {
  // ball 1
  x1 = limb1 * sin(angle1);
  y1 = limb1 * cos(angle1);

  // ball 2
  x2 = x1 + limb2 * sin(angle2);
  y2 = y1 + limb2 * cos(angle2);
}