Generating function, hamiltonian dynamics

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Homework Statement



A canonical transformation is made from (p,q) to (P,Q) through a generating function F=a*cot(Q), where 'a' is a constant. Express p,q in terms of P,Q.

Homework Equations





The Attempt at a Solution


A generating function is supposed to be a bridge between (p,q) and (P,Q), right? Now, if there is no functional dependence of F on p or q, that is the old variables, how is one supposed to find out the contact transformation asked for?
 
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yeah that generating function doesn't make sense. It should be F(q,Q) F(p,Q)

it has to be a function of two variables which connect the transformation Which the given does not
 
Thanks a lot! :)
 

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