论文标题
降低非独立系统的动量图
Momentum map reduction for nonholonomic systems
论文作者
论文摘要
本文介绍了非独立系统的减少程序，该系统承认合适类型的对称性和保守数量。完整的过程包含两个步骤。第一个（简单的）步骤会导致一个chaplygin系统，该系统由几乎符号结构描述，并带有其他对称性。本文的重点在于第二步，由马斯登·温斯坦（Marsden-Weinstein）组成 - 减少型，该型在[4,17]中概括了结构。在第二步中获得的几乎符号歧管被证明是与[7]中定义的降低的非循环括号的叶子相吻合。我们用几个古典例子说明了我们的构建。
This paper presents a reduction procedure for nonholonomic systems admitting suitable types of symmetries and conserved quantities. The full procedure contains two steps. The first (simple) step results in a Chaplygin system, described by an almost symplectic structure, carrying additional symmetries. The focus of this paper is on the second step, which consists of a Marsden-Weinstein--type reduction that generalizes constructions in [4,17]. The almost symplectic manifolds obtained in the second step are proven to coincide with the leaves of the reduced nonholonomic brackets defined in [7]. We illustrate our construction with several classical examples.
