Stability Analysis of the Helmholtz Oscillator with Time Varying Mass
Richard A. Morrison
Abstract
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.
Create a lesson
Related papers
Physical and emergent nonpairwise interactions in oscillator networks: from higher-order phase reduction to coupling design
Riccardo Muolo, Hiroya Nakao, Christian Bick
Degree Growth of Iterates of Curves and Likely Intersections
Sina Saleh, Jit Wu Yap
Infinite prime sumsets in structured and Uk(Φ)-uniform sets
Felipe Hernández, Tristán Radić
Long-Lived Carpet-Like Transients in Time-Dependent Modular Discrete Laplacian Dynamics
Małgorzata Nowak-Kępczyk
SIPHy: Sparse identification of port-Hamiltonian systems from noisy data
Håkon Noren Myhr, Sølve Eidnes, J. Nathan Kutz
Extended dynamic mode decomposition with Fourier dictionaries: Error bounds and fast implementation
Felix Bartel, Sandra Ritter, Manuel Schaller et al.