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Hamiltonian Systems with Symmetry and Their Reduction

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Part of the Lecture Notes in Physics book series (LNP,volume 707)

Abstract

In this chapter we shall give a brief description of classical Hamiltonian mechanics with symmetry, emphasizing the mechanics on cotangent bundles, the Hamiltonian reduction, the commutative and noncommutative integrability and the transition from quantum mechanics to classical one. Another purpose of this chapter is to fix some notations. Until indicated otherwise, the material of this chapter is quite standart and different parts of it could be found in [8, 32, 58, 193, 200] and many other sources. It will be used below in Chaps. 6 and 7 for studying the classical one- and two-body problems on two-point homogeneous Riemannian spaces.

Keywords

  • Hamiltonian System
  • Smooth Manifold
  • Symplectic Manifold
  • Poisson Structure
  • Symplectic Structure

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2006 Springer

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Shchepetilov, A.V. (2006). Hamiltonian Systems with Symmetry and Their Reduction. In: Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces. Lecture Notes in Physics, vol 707. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35386-0_4

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