Hamiltonian Classical Mechanics

Gerardo F. Torres del Castillo ()
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Gerardo F. Torres del Castillo: Universidad Autónoma de Puebla, Instituto de Ciencias

Chapter Chapter 8 in Differentiable Manifolds, 2012, pp 201-253 from Springer

Abstract: Abstract In this chapter we start by showing that any finite-dimensional differentiable manifold M possesses an associated manifold, denoted by T ∗ M, called the cotangent bundle of M, which has a naturally defined nondegenerate 2-form, which allows us to define a Poisson bracket between real-valued functions defined on T ∗ M. We then apply this structure to classical mechanics and geometrical optics, emphasizing the applications of Lie groups and Riemannian geometry. Here we will have the opportunity of making use of all of the machinery introduced in the previous chapters.

Keywords: Vector Field; Rigid Body; Poisson Bracket; Configuration Space; Symplectic Manifold (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8271-2_8

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DOI: 10.1007/978-0-8176-8271-2_8

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