ME 533
NONLINEAR DYNAMIC ANALYSIS

Course Description

Course focuses on understanding the behavior of nonlinear dynamic systems of interest to mechanical engineers.

Topics

• Linearization of nonlinear systems and linearized stability for both continuous and discrete systems
• Lyapunov stability analysis
• Bifurcations of equilibria
• Center manifold theory
• Properties of periodic solutions
• Perturbation theory: Regular, Lindstedt-Poincare, Multiple Scales
• Stability of periodic solutions via Floquet theory and Poincare maps

Learning Outcomes

The student, upon completion of this course, will be able to:

• Identify fixed points of nonlinear differential equations and mappings, and determine the stability of such points via linearization or Lyapunov theory.
• Identify and classify bifurcations in nonlinear differential equations and mappings.
• Use perturbation techniques to determine approximate solutions of nonlinear differential equations.
• Use Matlab to simulate and analyze the response of nonlinear systems.