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.

中文翻译：

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关于时变拉格朗日系统的混合Routh减少的注记

本说明讨论混合动力依赖时间的机械系统的Routh减少。我们给出了一般条件，即是否有可能通过对称来减少与时间有关的混合拉格朗日系统，从而扩展并统一连续时间系统的先前结果。我们以带有移动壁的台球为例说明该方法的适用性。