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Systems of ODEs: Imaginary Eigenvalues and Center Fixed Points

Systems of ODEs: Imaginary Eigenvalues and Center Fixed Points

Steve Brunton via YouTube Direct link

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Overview

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Systems of ODEs: Imaginary Eigenvalues and Center Fixed Points

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  1. 1 Overview
  2. 2 Examples of physical systems with complex eigenvalues
  3. 3 Quick recap of basic properties of complex numbers
  4. 4 Computing the eigenvectors
  5. 5 Writing the full solution
  6. 6 Geometric intuition: The solution is a rotation matrix
  7. 7 Adding small friction: Center becomes spiral sink

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