Cotangent Bundles

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


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.


Configuration Space Symplectic Form Symplectic Manifold Canonical Transformation Cotangent Bundle 
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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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