Double pendulum numerical solver that uses Runge-Kutta 4th Order methods for integration.
It plots the angles of the pendulums over time, the angular velocities
of the pendulums over time, and the trajectories of the pendulums by
plotting the x and y coordinates of the pendulums over time.
Description
A double pendulum is a physical system that consists of two connected pendulums. Wherein, each pendulum
has rod of specific length and a bob of specific mass. The motion of a double pendulum is sensitive to the
initial conditions (angles and angular velocities) of each pendulum. A small change in the initial conditions
of the system can lead to a considerable change in the motion of the system. In this sense, the motion of a
double pendulum exhibits chaotic behaviour.
Equations of Motion
The motion of a double pendulum is described by the following equations of motion: