Is There a Canonical Transformation for x = 2qa/sin(T) and p = 2qa.cos(T)?

[photomagnetic]

Homework Statement

Show that x = 2qa/sin(T) and p = 2qa.cos(T) is a canonical transformation
into new coordinates T and momentum q.

Homework Equations

The Attempt at a Solution

It looks easy, I've tried matrix/jacobi method, and symplectic method. But these two seem to be not canonical. Am I missing something? The question doesn't give anything else. Do I have to find a generating function to prove that they are canonical? But then it'd would be silly, because the professor is very clear about these things. If he wanted to see a F generating function he would have said so.

 

[MarcusAgrippa]

Clue: do you have any theorems that provide necessary and sufficient conditions for a transformation to be canonical?

 

[photomagnetic]

I re-correct myself, the prof. is an jerk. He hadn't mentioned that we had to use a generating function. now I got it. thanks anyway.

 

[MarcusAgrippa]

That's not nice. I'm sure your prof is a very nice fellow.

Incidentally, there are several different methods that you might have used to show that the given transformation is canonical.

 

[photomagnetic]

Yeah not telling which method we "must" use is not nice either.
Anyway after trying to do 3 hws each week, and spending a huge chunk of time,
people can get mad. Also no need to be politically correct here.