The dynamics of a constrained, nonlinear oscillator

This thesis examines the behavior of oscillating systems whose range of motion is constrained by forces that effectively act as soft constraints. For conservative systems, we shall show that for small constraints, the system has a family of periodic solutions in a neighborhood of an equilibrium. These periodic solutions can be approximated by a Poincare-Lindstedt expansion. In the case of damped motion, by examining the eigenvalues of the linearized system, one can infer information about the equilibria of the perturbed system.