info:eu-repo/semantics/article
Symmetries and periodic orbits in simple hybrid Routhian systems
Fecha
2020-05Registro en:
Colombo, Leonardo Jesus; Eyrea Irazu, Maria Emma; Symmetries and periodic orbits in simple hybrid Routhian systems; Elsevier; Nonlinear Analysis: Hybrid Systems; 36; 5-2020; 1-33
1751-570X
CONICET Digital
CONICET
Autor
Colombo, Leonardo Jesus
Eyrea Irazu, Maria Emma
Resumen
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.