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Hybrid dynamics of two coupled oscillators that can impact a fixed stop

Andre X. C. N. Valente·N. H. McCLamroch·Igor Mezic
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Abstract

We consider two linearly coupled masses, where one mass can have inelastic impacts with a fixed, rigid stop. This leads to the study of a two degree of freedom, piecewise linear, frictionless, unforced, constrained mechanical system. The system is governed by three types of dynamics: coupled harmonic oscillation, simple harmonic motion and discrete rebounds. Energy is dissipated discontinuously in discrete amounts, through impacts with the stop. We prove the existence of a nonzero measure set of orbits that lead to infinite impacts with the stop in a finite time. We show how to modify the mathematical model so that forward existence and uniqueness of solutions for all time is guaranteed. Existence of hybrid periodic orbits is shown. A geometrical interpretation of the dynamics based on action coordinates is used to visualize numerical simulation results for the asymptotic dynamics.

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Andre X. C. N. Valente, N. H. McCLamroch, Igor Mezic. 2003-09-23. Hybrid dynamics of two coupled oscillators that can impact a fixed stop. https://doi.org/10.1016/s0020-7462(01)00126-3

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