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Geometry of stroboscopic Poincare map for forced system
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Classroom Contents
Periodic Systems and Periodic Motion - Parametric Resonance Tongues of Instability, Mathieu Equation
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- 1 Time-periodic system introduction
- 2 Square wave forcing of simple harmonic oscillator
- 3 Forcing response diagram
- 4 eigenvalues of the mapping matrix M
- 5 Resonance tongues for square wave forcing
- 6 Stable and unstable examples of resonant motion
- 7 Going to sinusoidal forcing
- 8 Mathieu equation
- 9 Resonance tongues of instability
- 10 Kapitza pendulum - vibration-induced stability of inverted pendulum
- 11 Geometry of stroboscopic Poincare map for forced system
