Pendulum Simulation

This project is a set of physics simulations for three classic systems. A double pendulum. A spring pendulum. And an inverted pendulum. I started from scratch and wrote out the math myself instead of using a built in model. For each system, I chose the variables to describe the motion. I wrote the forces and energy relationships. Then I derived the differential equations that control how the system moves over time. After that, I implemented the equations in MATLAB. I used numerical solving to simulate the motion step by step. Then I plotted the results and created animations so the motion is easy to see. I also built the same systems in Simulink using block diagrams. This made it easy to change parameters and starting conditions and immediately see the effect in the simulation.