ME 6444 Nonlinear Systems

ME 6444: Nonlinear Systems
Offered as Required

Credit Hours:	3-0-3
Prerequisites:	Sufficient background in undergraduate mathematics; at least calculus through differential equations and linear algebra. Knowledge of computer packages such as MATLAB are strongly recommended, graduate standing.
Catalog Description:	Investigation of nonlinear systems using analytical and numerical techniques.
Textbook:	Dominic W. Jordan, Peter Smith, and P. Smith; Nonlinear Ordinary Differential Equations, 3rd Edition, Oxford University Press, 1999.
Instructor:	Aldo Ferri

Course Outline:

Introduction; properties of nonlinear systems
Phase portraits for second order systems; characterization of singular points and local stability; first and second methods of Lyapunov
Limit cycles; Poincaré Index; Poincaré-Bendixon Theorem
Time-integration techniques for nonlinear initial value problems
Averaging techniques
Perturbation methods
Harmonic balance and sinusoidal describing functions
Subharmonic and superharmonic response to sinusoidal excitation
Parametric excitation; Mathieu/Hill equations; Floquet theory.
Partial differential equations; Perturbation methods, Galerkin methods.

Grading: Homework 20%, Midterm 30%, Final 50%

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Revised June 2004