A perturbation analysis of constrained nonlinear vibrations

We examine a nonlinear differential equation that is motivated by the use of soft constraints in the study of human movement. We investigate various properties of the system when considering the effects of forcing and damping. For the unforced and undamped problem, we implement two methods for approximating periodic solutions. We also address the stability properties of the unforced problem and show that no limit cycles can exist in the presence of damping. However, limit cycles can exist for the forced problem, and these are studied by use of the harmonic balance method.