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.
Textbooks: Dominic W. Jordan, Peter Smith, and P. Smith; Nonlinear Ordinary Differential Equations, 3rd Edition, Oxford University Press, 1999.
Instructors: Aldo Ferri
Topics:
  • 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; PoincarĂ© Index; PoincarĂ©-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 Scheme (%):

Homework

20

Midterm

30

Final

50