拟不变拉格朗日量的Routhian约化
Routhian reduction for quasi-invariant Lagrangians
摘要：
本文将Routhian约化描述为标准辛约化的一种特殊情况，也称为Marsden-Weinstein约化。我们使用这种对应关系，提出了一个推广的Routhian减少准不变的拉格朗日，即拉格朗日不变的总时间导数。我们展示了如何功能Routhian减少可以被看作是一个特定的实例减少一个准不变的拉格朗日，我们展示了一个Routhian减少过程的特殊情况下的拉格朗日与准循环坐标。作为应用，我们考虑了带电粒子在磁场中的动力学。
英文摘要：
In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total time derivative. We show how functional Routhian reduction can be seen as a particular instance of reduction of a quasi-invariant Lagrangian, and we exhibit a Routhian reduction procedure for the special case of Lagrangians with quasi-cyclic coordinates. As an application we consider the dynamics of a charged particle in a magnetic field.
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