Nonlinear (Flight) Dynamics (AERO 660)

by Dr. Tamas Kalmar-Nagy

  • One dimensional flows
         – Fixed points and stability
         – Linear stability analysis
         – Existence and uniqueness
         – Scaling and dimensional analysis
         – Bifurcations: saddle-node, transcritical and pitchfork
         – Imperfect bifurcations and catastrophes

  • Two dimensional flows
         – Fixed points and phase portraits
         – Linear systems and their classification
         – Conservative and reversible systems, index theory
         – Limit cycles: Poincare-Bendixson Theorem, Van der Pol oscillator, Lienard systems, relaxation oscillators, weakly nonlinear oscillators
         – Perturbation theory, Poincare-Lindstedt method, averaging, method of multiple scales
         – Duffing equation, forcing and resonance

  • Higher dimensional systems
         – Hopf bifurcations
         – Center manifold theory
         – Lorenz equation, quasi-periodicity and chaos
         – Lorenz map, Poincare map, fixed points and cobwebs, Logistic map, periodic windows and Lyapunov exponent
         – Two dimensional maps
         – Fractals, Cantor set and dimensions
         – More on strange attractors and chaos