made by Hsing Lo
equations from myPhysicsLab

This is a double pendulum simulator built by Hsing Lo heavily adapting differential equations from myPhysicsLab. A double pendulum, mathmatically a four-dimentional system, is a chaotic system that is often used as a demonstration for chaos because of its mesmerizing path and intuitiveness as a physical contraption. This simulation simulates one or more double pendulums showing its chaotic patterns and divergent tendency. This simulation uses Euler's method to estimate differential equations, iterating the equations (at a default of) 1024 times per frame, or around 60000 times per second. A pendulum's state is projected to two dimensions while assuming no friction, perfectly rigid and massless joints, point masses, perfectly and uniform gravity, all under classical mechanics; an simple implemention for drag is included but not accessable to the user.

Below are some physics data in case you are interested. With the exception of energy, they are all internally used. Units are up to the viewer's discretion as long as they are coherent. Data updated every frame.

The unit is any coherent unit. Radian is implied for angles, the direction is counterclockwise; 0 is hanging. Positive values for g (acceleration due to gravity) describes downwards acceleration. The reference line for gravitional potential energy is the center of all pendulums (pivot of the inner bob). The translational reference for kinetic energy is the center of all pendulums and the rotational reference is the canvas.
†This ratio of energy has 0 set as a stationary hanging pendulum; the gravitional potential energy used to calculate it is different from what is displayed with its 0 set to the minimum possible.

Double Pendulum Simulator

Preset starting parameter

Set custom starting parameters (default values used when fields blank)

Environment (click to set)

Arm 1 length; Arm 2 length;
Mass 1 mass; Mass 2 mass;