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Classical Two-Body Problem on Two-Point Homogeneous Riemannian Spaces

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

Abstract

In this chapter we consider the classical two-body problem on two-point homogeneous Riemannian spaces. First we derive an expression of its Hamiltonian function through the canonical variables r, p r , corresponding to the radial degree of freedom, and generators of the Poisson algebra PI (QS) ≌ gr DiffI (QS). Here we use the dequantization procedure from Sect. 4.3.3 since it allows one to avoid quite cumbersome calculations similar to those in Chap. 5. Also, one gets integrals of motion from central elements of the algebra DiffI (QS), constructed in Chap. 3.

Keywords

  • Rigid Body
  • Mass Center
  • Hamiltonian Function
  • Additional Relation
  • Poisson Algebra

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Shchepetilov, A.V. (2006). Classical Two-Body Problem on Two-Point Homogeneous Riemannian Spaces. 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_7

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