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

Communicated by Manuel de León

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

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  • 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.

    Mathematics Subject Classification: Primary: 70S10, 37J15; Secondary: 70H03.

    Citation:

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  • Figure 1.  A "billiard" with moving walls

    Figure 2.  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

    Figure 3.  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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