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: pubs.aip.org/a...
Get the basics of the pendulum model: • The Pendulum - Dynamic...
Lecture series on dynamical systems: • Welcome - Dynamical Sy...
Lectures series on differential equations: • Welcome - Ordinary Dif...
More information on the instructor: hybrid.concord...
Follow @jbramburger7 on Twitter for updates.