Analyzing chaos in the double pendulum

\\ \\ In this presentation, I will show the results of the project that I worked on during the computational physics course I am attending at Universidad de Colima. The goal of the project is to develop a code in Python that solves the equations of motion of the double pendulum and finds the conditions in which this system exhibits chaos. Chaotic behavior in a dynamical system occurs when there exists a significant dependence on initial conditions of the system evolution. In this work, I obtained the equations of motion using Lagrangian and Hamiltonian mechanics and solved them using numerical methods. There are different ways of detecting this type of behavior and, in this project, I used three tools to find chaos in the double pendulum: phase space plots, Lyapunov exponents, and Poincare sections. I found interesting curves for different initial conditions and I made animations comparing the behavior of different pendulums with slightly different initial conditions in order to understand, in a more visual way, how significant is the difference in the behavior of each one. Even though this project addresses a system that is well studied in the literature, it allows us to learn to code in Python and how to use the numerical methods seen during the course.