The course covers the analysis of time-dependent systems, particularly focusing on periodic time-dependence. Students will learn about parametric resonance, Mathieu equation, and the vibration-induced stability of the inverted pendulum using the Kapitza pendulum. The teaching method involves lectures with examples and diagrams. This course is intended for graduate students studying advanced dynamics, Hamiltonian systems, and nonlinear dynamics.
Periodic Systems and Periodic Motion - Parametric Resonance Tongues of Instability, Mathieu Equation
Overview
Syllabus
Time-periodic system introduction.
Square wave forcing of simple harmonic oscillator.
Forcing response diagram.
eigenvalues of the mapping matrix M.
Resonance tongues for square wave forcing.
Stable and unstable examples of resonant motion.
Going to sinusoidal forcing .
Mathieu equation.
Resonance tongues of instability.
Kapitza pendulum - vibration-induced stability of inverted pendulum.
Geometry of stroboscopic Poincare map for forced system.
Taught by
Ross Dynamics Lab
