Time reversal symmetries and zero dynamics for simple hybrid Hamiltonian control systems

This paper studies Hamel's formalism for simple hybrid mechanical control systems and explores the role of time-reversal symmetries and hybrid zero dynamics to predict the existence of periodic orbits in these control system. A time reversal symmetry in the phase-space permits us to construct a time reversible hybrid Hamiltonian system. If the Hamiltonian function describing the continuous dynamics and the impact map are invariants under a time reversal symmetry on the zero hybrid dynamics, under some mild conditions, we find sufficient conditions for the existence of periodic solutions for the class of simple hybrid Hamiltonian control systems.

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