double-pendulum-simulation

Note: A detailed PDF report for this project is included in this repository.

A double pendulum simulation in MATLAB which demonstrates the chaotic nature of the system

Parameters to change the initial conditions of the double pendulum system:

Global variables:

• L1: Length of first ball
• L2: Length of second ball
• m1: Mass of first ball
• m2: Mass of second ball
• g: Acceleration due to gravity

Initial conditions of the system:

• th1(1): Initial angle of the first ball from the vertical in radians
• th2(2): Initial angle of the second ball from the vertical in radians
• w1(1): Initial angular velocity of the first ball
• w2(1): Initial angular velocity of the second ball

Properties of the simulation runtime:

• time: How long the simulation will run in seconds (represents the system's simulation accurately for "time" seconds; doesn't actually run in real-time "time" seconds)
• timeStep: Step size of time increment for the ODE solvers

Choice of ODE solver:

• Euler's Method: A first-order ode solver method which is less accurate and not desirable for chaotic systems given the large impact small changes lead to
• 4th-order Runge-Kutta (RK4): A fourth-order ode solver method that gives much more accurate results with minimal truncation errors

The preferred ode-solver method can be chosen by commenting out the other method in the main file. By default, "Euler's Method" is commented out and RK4 is used.