Drawing Phase Portraits for Nonlinear Systems

Learn how to draw phase portraits and analyze fully nonlinear systems in this comprehensive video tutorial. Discover techniques for identifying fixed points, linearizing around them, and analyzing stability using eigenvalues and eigenvectors. Explore the process of inferring global nonlinear dynamics outside linearized regions. Follow along as the instructor derives equations from F=ma, finds system fixed points, and demonstrates linearization techniques. Examine the characteristics of a linear center and an unstable saddle as fixed points. Gain insights into drawing complete global phase portraits and observe how adding friction affects the system dynamics. Master the skills needed to visualize and understand complex nonlinear system behavior through phase portrait analysis.

Overview and deriving equations from F=ma
Finding fixed points of system
Linearizing near fixed points
First fixed point: A linear center
Second fixed point: An unstable saddle
Drawing full global phase portrait
Adding friction and drawing phase portrait