2x2 Systems of ODEs: Saddle Points and Instability

This video investigates a 2-dimensional linear system of ordinary differential equations with a positive and a negative real eigenvalue. These solutions are known as unstable saddle points. Saddle points are extremely useful for energy-efficient transport, including for bipedal walking and locomotion, for fight jets, and also for interplanetary transport. We investigate the solutions using eigenvalues and eigenvectors, as well as with phase portrait pictures.

Playlist: https://www.youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/

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0:00 Overview of saddle points
4:52 Drawing a saddle in phase space
10:52 Saddle example: Human walking
14:42 Saddle example: Particle in a potential well
17:24 Saddle example: Planetary transport in the solar system

Видео 2x2 Systems of ODEs: Saddle Points and Instability канала Steve Brunton