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Drawing Phase Portraits for Nonlinear Systems

Steve Brunton via YouTube

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Overview

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This course demonstrates how to analyze a nonlinear particle system by finding fixed points, linearizing near them, using eigenvalues and eigenvectors to assess stability, and inferring global phase portraits. It also examines how friction changes center behavior into a stable spiral.

Syllabus

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

Taught by

Steve Brunton

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