This video introduces students to the notion of stability of equilibria. A temperature example is explored using an energy argument, and then the typical linear stability analysis framework is introduced. This framework is applied in detail to analyze a pendulum.
After watching this video students will be familiar with the framework of equilibrium and stability analysis.
Funding provided by the Singapore University of Technology and Design (SUTD)
Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD
MIT © 2012
It is highly recommended that the video is paused when prompted so that students are able to attempt the activities on their own and then check their solutions against the video.
During the video, students will:
- Identify whether two equilibria for a physical model are stable or unstable based on physical intuition.
- Find a linear approximation for the sine function near 0.
- Determine what happens to the solution when both eigenvalues for the eigenproblem near the equilibrium have negative real part.
- Determine what happens to the solution when at least one eigenvalue has positive real part.
- Determine what happens to the solution when the eigenvalues have zero real part.
- Work through the linear stability analysis framework for the top equilibrium of the pendulum.