Scholarlink

In this chapter, which aims to set a convenient framework for the study of the class of Hamiltonian systems with symmetries, the definition of Hamiltonian G-action and of moment map will be introduced. The former provides a geometrical model for the notion of symmetry in Hamiltonian mechanics, the latter is a broad generalization of the concepts of linear and angular momenta, and it provides a geometrical setting where the symmetries become an efficient a tool to solve the Hamilton equations. In particular, as it will be emphasized hereafter, the moment map is the main ingredient in the theory of the Hamiltonian reduction which, besides its applications to dynamics, is one of the more, if not the most, efficient tool to produce new symplectic manifolds from old ones.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Hamiltonian G-Actions and the Marsden-Weinstein-Meyer Reduction

  • 章节

  • 发表日期：

    2026年

查看全文
  • Alessandro Arsie,
  • Igor Mencattini

摘要

In this chapter, which aims to set a convenient framework for the study of the class of Hamiltonian systems with symmetries, the definition of Hamiltonian G-action and of moment map will be introduced. The former provides a geometrical model for the notion of symmetry in Hamiltonian mechanics, the latter is a broad generalization of the concepts of linear and angular momenta, and it provides a geometrical setting where the symmetries become an efficient a tool to solve the Hamilton equations. In particular, as it will be emphasized hereafter, the moment map is the main ingredient in the theory of the Hamiltonian reduction which, besides its applications to dynamics, is one of the more, if not the most, efficient tool to produce new symplectic manifolds from old ones.