In this lecture we consider one of the oldest and best-studied mechanical systems: the pendulum. We begin with the conservative pendulum model, meaning there is no energy dissipation due to friction or air resistance. We sketch out the phase plane and explain what each of the trajectories means for the physical pendulum. We then conclude with a discussion of what are the effect of damping terms in the model.
Deriving the equation for the pendulum from physical laws: https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Scientific_Computing_(Chasnov)/II%3A_Dynamical_Systems_and_Chaos/10%3A_The_Simple_Pendulum
Video abstract by Dr. Kaheman on building and controlling the double pendulum on a cart: https://www.youtube.com/watch?v=OkEsTLeIP98
How to build your own pendulum on a cart: https://www.sciencedirect.com/science/article/pii/S246806722300072X
How the motion of the double pendulum in phase space is almost the same space travel: https://link.springer.com/article/10.1007/s11071-023-08232-0
This course is taught by Jason Bramburger for Concordia University.
More information on the instructor: https://hybrid.concordia.ca/jbrambur/
Follow @jbramburger7 on Twitter for updates.
