The Driven Pendulum - Dynamical Systems Extra Credit | Lecture 8

In this lecture we apply many of the techniques we have learned so far to understand the physical motion of a pendulum model with constant driving torque. We begin by presenting the model and analyzing its fixed points. We then proceed to identify limit cycles, which are proven to exist using a Poincare map. It is also shown that depending on the damping coefficient the limit cycle disappears through either a homoclinic bifurcation or from a saddle-node bifurcation of fixed points on it. Thus, we have a practical example of the limit cycle bifurcations from the previous lecture. Learn about the derivation of the torque driven pendulum: https://pubs.aip.org/aapt/ajp/article... Get the basics of the pendulum model:    • The Pendulum - Dynamical Systems | Lecture 19   Lecture series on dynamical systems:    • Welcome - Dynamical Systems | Intro Lecture   Lectures series on differential equations:    • Welcome - Ordinary Differential Equations ...   More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.