most recent 30 from http://mathoverflow.net 2013-05-25T15:09:02Z http://mathoverflow.net/feeds/user/10301 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17325/why-is-cotangent-more-canonical-than-tangent/43420#43420 Sina 2010-10-24T19:28:48Z 2010-10-24T19:28:48Z

<p>The canonicity comes in terms of the symplectic structure. On cotangent bundle there is a canonical symplectic form that is independent of the hamiltonian where as on tangent bundle the symplectic form is dependent to the lagrangian. </p> <p>Or put in another words because the cotangent bundle itself is already built from some 1-forms attached to each points, it is easy to build a symplectic from the cotangent bundle itself while since the tangent bundle is made of tangent vectors attached to each point, you need the help of a function to build a symplectic two form on it. </p>