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Systems of ODEs: Imaginary Eigenvalues and Center Fixed Points

Steve Brunton via YouTube

Overview

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This course explains how to solve a two-dimensional linear system of ordinary differential equations with a purely imaginary complex-conjugate eigenvalue pair. It derives real-valued solutions, interprets them as rotations and neutrally stable center fixed points, and shows how friction changes the center into a spiral sink.

Syllabus

Overview
Examples of physical systems with complex eigenvalues
Quick recap of basic properties of complex numbers
Computing the eigenvectors
Writing the full solution
Geometric intuition: The solution is a rotation matrix
Adding small friction: Center becomes spiral sink

Taught by

Steve Brunton

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