# Hamiltonian system: match transformations and constants of motion

I have a problem about the interpretation of an exercise.

Given the following Hamiltonian

$$H=\frac{\mathbf{p_0}^2}{2m}+\frac{\mathbf{p_1}^2}{2m}+\frac{\mathbf{p_2}^2}{2m}-2V(\mathbf{r_1}- \mathbf{r_0})+V(\mathbf{r_2}-\mathbf{r_1})$$

where $$V(\mathbf x)=\frac {e^2}{|\mathbf x|}.$$

I have to

enumerate all the continue transformation such as the form of H remains unchanged and match to each one a costant of motion.

I have thought that the form of H remains unchanged for translation and rotation, but I don't know how I can match a constant of motion. Is "constant of motion" linked to "generating function of the transformation"?

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Related question by OP: physics.stackexchange.com/q/66717/2451 and links therein. –  Qmechanic Jun 1 '13 at 21:59