Symmetries and periodic orbits in simple hybrid Routhian systems. (May 2020)

• Record Type: Journal Article
• Authors: Colombo, Leonardo J.; Eyrea Irazú, María Emma
• Is Part Of: Nonlinear analysis. Volume 36(2020)
• Publication Date: 2020-05
• Subjects: primary 37K05 -- secondary 37J15 37N05 34A38 34C14 34C25; Hybrid systems -- Symmetries -- Routh reduction -- Poincaré map; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100857
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics is 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 hybrid Routhian reduction . In this paper we study sufficient conditions for the existence of periodic orbits in hybrid Routhian systems which also exhibit a 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.