Regular Symplectic Reduction Theory

  • Juan-Pablo Ortega
  • Tudor S. Ratiu
Part of the Progress in Mathematics book series (PM, volume 222)

Abstract

In this chapter we present the most elementary version of symplectic reduction using standard momentum maps. The symplectic reduction method represents a generalization and synthesis of various techniques of elimination of variables from classical mechanics that are based on the existence of conserved quantities. Early specific examples are the reduction to the center of mass frame in the n-body problem using translational invariance and Jacobi’s elimination of the node that allows the elimination of four variables using rotational invariance.

Keywords

Vector Bundle Poisson Bracket Symplectic Form Symplectic Manifold Cotangent Bundle 
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Copyright information

© Juan Pablo Ortega and Tudor S. Ratiu 2004

Authors and Affiliations

  • Juan-Pablo Ortega
    • 1
  • Tudor S. Ratiu
    • 2
  1. 1.CNRS-Laboratoire de Mathématiques de BensançonUniversité de Franche-Comté, UFR des Sciences et TechniquesBensançon CedexFrance
  2. 2.Départment de MathématiquesLausanneSwitzerland

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