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## Main Question or Discussion Point

I am using Jose & Saletan's "Classical Dynamics", where they introduce a rather contrived Hamiltonian in the problem set: [tex] H(q_1,p_1,q_2,p_2) = q_1p_1-q_2p_2 - aq_1^2 + bq_2^2 [/tex] where a and b are constants. This Hamiltonian has several constants-of-motion, including f = q

Since this Hamiltonian is a function of four variables, is there some theorem that says there are at most four functionally independent constants of motion? If not, then how would I know when I have found enough to form a basis?

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Note: The authors define functions f and g to be functionally independent if both functions can be written as functions of a third function. It would seem that this is a relatively obscure topic.

_{1}q_{2}, as can be easily checked. In fact, at this point I am aware of four "functionally independent" constants of motion.Since this Hamiltonian is a function of four variables, is there some theorem that says there are at most four functionally independent constants of motion? If not, then how would I know when I have found enough to form a basis?

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Note: The authors define functions f and g to be functionally independent if both functions can be written as functions of a third function. It would seem that this is a relatively obscure topic.