Nonlinear (Flight) Dynamics (AERO 660)

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