Double Pendulum

A double pendulum is composed of one pendulum suspended from another pendulum. Although its behaviour is completely deterministic, a small change in the initial conditions will drasticallly affect the behaviour of the system later on. This phenomenon is known as chaos. Due to this, making long-term predictions for a chaotic system's behaviour is meaningless. In the below simulation, we have two double pendulums such that their initial conditions differ by a small value. Observe how this small difference leads to a drastic change in the pendulum's trajectory.



Pressing 'Restart' button will reset the simulation to the initial state

Blue Pendulum:

Red Pendulum:

Modifying any parameters above or below, will automatically pause the simulation. Click on 'Resume' button to start simulation


Use these fields to set values with high precision:

Blue pendulum

θ1 (in degrees)

θ2 (in degrees)

Red pendulum

θ1 (in degrees)

θ2 (in degrees)

Note:
  1. You can choose any values of θ1 and θ2 for the two double pendulums. However, for observing the phenomenon of chaos, they need to differ from each other by a small value.
  2. Under the above circumstances, it may take a couple of oscillations of the double pendulum for their behaviours to diverge.
  3. Dynamics of the two bobs of the each double pendulum can be obtained from here. This simulation uses the equations of motion derived using Lagrangian mechanics.
  4. Related: Conway's Game of Life, Lorenz System, Planetary Motion.

Developed by ChanRT | Fork me at GitHub