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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
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