- #1
Klaus_Hoffmann
- 86
- 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.
[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.