Talk:Liouville dynamical system


 * I'm not sure if the solution is formulated clearly. First of all, where does m and a come from in

\frac{ma^{2}}{2} \left( \cosh^{2} \xi - \cos^{2} \eta \right)^{2} \dot{\xi}^{2} = E \cosh^{2} \xi + \left( \frac{\mu_{1} + \mu_{2}}{a} \right) \cosh \xi - \gamma $$



\frac{ma^{2}}{2} \left( \cosh^{2} \xi - \cos^{2} \eta \right)^{2} \dot{\eta}^{2} = -E \cos^{2} \eta + \left( \frac{\mu_{1} - \mu_{2}}{a} \right) \cos \eta + \gamma $$

Y was defined without them, so how can they appear in equations above?

Also I can't see the solution in:

u = \int \frac{d\xi}{\sqrt{E \cosh^{2} \xi + \left( \frac{\mu_{1} + \mu_{2}}{a} \right) \cosh \xi - \gamma}} = \int \frac{d\eta}{\sqrt{-E \cos^{2} \eta + \left( \frac{\mu_{1} - \mu_{2}}{a} \right) \cos \eta + \gamma}}. $$ What happened to Y which should be on the left side along with :$$\sqrt{2}$$? Was it replaced with u by some change of variables? If that's the case then u depends on xi and eta thus xi and eta cannot be expressed in terms of u. I could really use contents of this article in my work, so I hope that these uncertainties could be solved:) Regards. Avalokitesvara (talk) 21:21, 7 May 2009 (UTC)