Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Classical mechanics and Geommetry

  1. Aug 7, 2007 #1
    Given the Hamiltonian of a system [tex] \mathcal H [/tex] , could we obtain the curves solution to Hamilton equations X(t) Y(t) Z(t) as the Geodesic of a certain surface with Christoffle symbols [tex] \Gamma ^{i} _{jk} [/tex] i mean the curve X(t) satisfies the equation:

    [tex] \nabla _{x(t)} X(t)=0 [/tex] (covariant derivative vanishes)

    Also given the 1-form [tex] \theta =p^{i}dq^{i}-Hdt [/tex] and some elements of Diff. Geommetry how could solve our physical system ?? or reduce the solutions for x,y,z to 'Quadratures' ?? thanks.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Classical mechanics and Geommetry
  1. Classical Mechanics (Replies: 9)

  2. Classical Mechanics (Replies: 2)