# American Institute of Mathematical Sciences

June  2020, 12(2): 309-321. doi: 10.3934/jgm.2020014

## A note on Hybrid Routh reduction for time-dependent Lagrangian systems

 1 Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, Calle Nicolás Cabrera 13-15, Cantoblanco, 28049, Madrid, Spain 2 Department of Mathematics, Universidad Nacional de La Plata, Calle 1 y 115, La Plata 1900, Buenos Aires, Argentina 3 Departamento de Matemática, Universidad Nacional del Sur, Av. Alem, 1253, 8000 Bahía Blanca, Argentina

Communicated by Manuel de León

Received  December 2019 Revised  March 2020 Published  June 2020

Fund Project: L. Colombo was partially supported by I-Link Project (Ref: linkA20079) from CSIC, Ministerio de Economia, Industria y Competitividad (MINEICO, Spain) under grant MTM2016- 76702-P; "Severo Ochoa Programme for Centres of Excellence" in R & D (SEV-2015-0554). The project that gave rise to these results received the support of a fellowship from "La Caixa" Foundation (ID 100010434). M.E. Eyrea Irazú was partially supported by CONICET Argentina

This note discusses Routh reduction for hybrid time-dependent mechanical systems. We give general conditions on whether it is possible to reduce by symmetries a hybrid time-dependent Lagrangian system extending and unifying previous results for continuous-time systems. We illustrate the applicability of the method using the example of a billiard with moving walls.

Citation: Leonardo J. Colombo, María Emma Eyrea Irazú, Eduardo García-Toraño Andrés. A note on Hybrid Routh reduction for time-dependent Lagrangian systems. Journal of Geometric Mechanics, 2020, 12 (2) : 309-321. doi: 10.3934/jgm.2020014
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##### References:
A "billiard" with moving walls
Simulation for $c = 0.25$. The figure in the left corresponds with the reduced trajectory while the figure to the right corresponds with the reconstructed solution
Simulation for $c = 0.10$. he figure in the left corresponds with the reduced trajectory while the figure to the right corresponds with the reconstructed solution
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