This project contains an interactive and animated MATLAB script that simulates the motion of a double pendulum — a classic example of a chaotic system in physics.

Imagine two masses hanging from ropes, with one rope attached to the other in sequence. When released, the weights swing back and forth in a highly complex and unpredictable way. This system is very sensitive to initial conditions and is a textbook example of deterministic chaos.

• pendulum.m: the only file in the project. It contains the full simulation logic, animation, and plotting routines.

1. When you run pendulum.m, the program asks for the desired simulation duration.
2. It then solves a system of differential equations that governs the motion of the double pendulum.
3. The animation shows the pendulums moving in real time.
4. At the end:
   • If the simulation completes normally, a single graph is displayed showing the full trajectory.
   • If the simulation is stopped early, two plots appear:
     • One showing the trajectory up to the stopping point.
     • Another showing the full potential trajectory (as if the simulation had run to the end).

• MATLAB (R2020a or later is recommended)

This project is great for visualizing the behavior of nonlinear systems and exploring the concept of chaos. It can be used for educational purposes or simply as a scientific curiosity.