Symmetries and periodic orbits in simple hybrid Routhian systems

Abstract

Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a Lagrangian function, with a cyclic variable, the degrees of freedom for the corresponding hybrid Lagrangian system can be reduced by means of a method known as \textit{hybrid Routhian reduction}. In this paper we study sufficient conditions for the existence of periodic orbits in hybrid Routhian systems which also exhibit time-reversal symmetry. Likewise, we explore some stability aspects of such orbits through the characterization of the eigenvalues for the corresponding linearized Poincaré map. Finally, we apply the results to find periodic solutions in underactuated hybrid Routhian control systems.

arXiv commentNonlinear Analysis: Hybrid Systems 36, 100857, 2020

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Cited by in corpus (6)

• Nonsmooth Herglotz variational principle
• Hamilton-Jacobi theory for nonholonomic and forced hybrid mechanical systems
• Continuation of Periodic Orbits in Conservative Hybrid Dynamical Systems and its Application to Mechanical Systems with Impulsive Dynamics
• Hybrid Routhian reduction for simple hybrid forced Lagrangian systems
• On the integrability of hybrid Hamiltonian systems
• Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions