Systems of ODEs - Saddle Points and Instability

Explore the concept of unstable saddle points in 2-dimensional linear systems of ordinary differential equations. Delve into the characteristics of solutions with positive and negative real eigenvalues. Discover the practical applications of saddle points in energy-efficient transport, including bipedal walking, fighter jet maneuvers, and interplanetary travel. Examine solutions using eigenvalues, eigenvectors, and phase portrait visualizations. Learn how to draw saddles in phase space and study real-world examples such as human locomotion, particle behavior in potential wells, and planetary movement within the solar system.

Overview of saddle points
Drawing a saddle in phase space
Saddle example: Human walking
Saddle example: Particle in a potential well
Saddle example: Planetary transport in the solar system