41 questions linked to/from Which transformations are canonical?
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Condition for a time-dependent transformation to be a canonical transformation [duplicate]

I'm looking for a sufficient condition to determine if a given transformation is a canonical transformation. I have found two conditions, but they are only valid for the case that the transformation ...
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Time Dependence on Landau & Lifshitz's Proof of Poisson's Bracket Canonical Invariance

I'm reading Landau & Lifshitz's Mechanics and, at a certain point when discussing canonical transformations, they prove that Poisson brackets are canonical invariants. The proof starts with ...
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Generating function for canonical transformation

Short version: I've been reading through some notes on integrable systems/Hamiltonian dynamics, and am stuck on a problem: Show that the coordinate transformation derived via the generating function ...
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Are all time-independent Hamiltonian systems related locally via time-independent canonical transformation?

So recently I've been doing some self-study on canonical transformations and relating together different Hamiltonian systems. I've found this paper (PDF) with a remarkable result showing that any two ...
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If $(q,p)$ to $(Q,P)$ is a canonical transformation, then does this imply $(Q,P)$ to $(q,p)$ is also?

If $(q,p)$ to $(Q,P)$ is a canonical transformation, then does this imply $(Q,P)$ to $(q,p)$ is also, assuming Hamilton's equations hold for the coordinates $(q,p)$? This seems like it should be true ...
My professor mentioned: A simple way of testing whether a mapping $(q,p)$ to $(Q,P)$ is canonical is by examining: $$P · dQ − p · dq$$ and if it equals to $dA$ (a differential) then it is canonical. ...
In Goldstein's mechanics book he defines a canonical transformation as a transformation from $q, p$ to $Q, P$ with $$Q = Q(q,p,t) \tag{9.4a}$$ and $$P = P(q,p,t) \tag{9.4b}$$ such that if $H$ ...