The Interplay Between Symmetries and Impact Effects on Hybrid Mechanical Systems

2024/03/19 by William Clark, Clark, William, Leonardo Colombo +3
Engineering · #Differential Geometry (math.DG) #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #FOS: Mathematics #Mechanical Engineering and Vibrations Research #Mechanics and Biomechanics Studies #Robotics (cs.RO)

paper · pdf · doi:10.48550/arxiv.2403.12842

openalex publication_date 2024/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Hybrid systems are dynamical systems with continuous-time and discrete-time components in their dynamics. When hybrid systems are defined on a principal bundle we are able to define two classes of impacts for the discrete-time transition of the dynamics: interior impacts and exterior impacts. In this paper we define hybrid systems on principal bundles, study the underlying geometry on the switching surface where impacts occur and we find conditions for which both exterior and interior impacts are preserved by the mechanical connection induced in the principal bundle.

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