Autoparametric quasiperiodic excitation

The dynamics of an autonomous conservative three degree of freedom system which exhibits autoparametric quasiperiodic excitation is investigated. The system is a generalization of a classical system known as the “particle in the plane”. The system exhibits a motion, the z=0z=0 mode, whose stability is governed by a linear second order ODE with quasiperiodic coefficients. The behavior of the latter ODE is studied by using three different methods: numerical integration, harmonic balance and perturbation methods.