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Cotangent Bundles

  • Jerrold E. Marsden
  • Tudor S. Ratiu
Chapter
  • 2.5k Downloads
Part of the Texts in Applied Mathematics book series (TAM, volume 17)

Abstract

In many mechanics problems, the phase space is the cotangent bundle T*Q of a configuration space Q. There is an “intrinsic” symplectic structure on T*Q that can be described in various equivalent ways. Assume first that Q is n-dimensional, and pick local coordinates (q 1, ... ,q n ) on Q. Since (dq 1 , ... , dq n ) is a basis of T q * Q, we can write any α ∈ T q * Q as α = p i dq i This procedure defines induced local coordinates (q 1, ... , q n , p 1, ... , p n ) on T*Q.

Keywords

Configuration Space Symplectic Form Symplectic Manifold Canonical Transformation Cotangent Bundle 
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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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Jerrold E. Marsden
    • 1
  • Tudor S. Ratiu
    • 2
  1. 1.California Institute of TechnologyControl and Dynamical Systems, 107-81PasadenaUSA
  2. 2.Département de mathématiquesEcole polytechnique fédérale de LausanneLausanneSwitzerland

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