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:(adsbygoogle = window.adsbygoogle || []).push({});

[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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Classical mechanics and Geommetry

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**