Stability Analysis of the Helmholtz Oscillator with Time Varying Mass

Details Stability Analysis of the Helmholtz Oscillator with Time Varying Mass Stability Analysis of the Helmholtz Oscillator with Time Varying Mass

2007-01-21

arxiv.org/abs/math/0701593v1

Mathematics

Dynamical Systems

10 pages, 7 figures

Scientific paper

We study the effects of periodically time varying mass on the stability of the Helmholtz oscillator, which, when linearised, takes the form of Ince's equation and exhibits parametric resonance. The resonance regions in the parameter space are mapped and we use the Melnikov function to demonstrate that the parametric instability does not affect the qualitative dynamics of the nonlinear system.

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