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

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

2003-09-23

arxiv.org/abs/nlin/0309060v1

International Journal of Non-Linear Mechanics 38, 677-689 (2003)

Nonlinear Sciences

Chaotic Dynamics

23 pages, 7 figures. Feedback welcome

Scientific paper

10.1016/S0020-7462(01)00126-3

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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