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A newtonian system mathematically always a trivial bundle?

  1. Jan 24, 2015 #1
    The phase space of a Newtonian system is a cotangent bundle, where the base space is the manifold M of the configuration space (the positions) and the typical fiber is the cotangent space T*M (the momenta). Is it always the case that this cotangent bundle is the trivial bundle M x TM?
  2. jcsd
  3. Jan 24, 2015 #2
    No. The cotangent bundle is homeomorphic to the tangent bundle and tangent bundles are not always trivial. M cross TM is the manifold cross the tangent bundle, which is not what you want to say there.
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