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

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Homework Help Overview

The problem involves demonstrating that the transformation defined by x = 2qa/sin(T) and p = 2qa.cos(T) is a canonical transformation into new coordinates T and momentum q. The context is within the subject area of classical mechanics, specifically Hamiltonian mechanics.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss various methods to prove the transformation is canonical, including the matrix/jacobi method and the symplectic method. There is uncertainty about whether a generating function is necessary for the proof, and some participants express frustration over the lack of explicit instructions from the professor.

Discussion Status

The discussion reflects a mix of attempts to understand the requirements for proving the transformation's canonical nature. Some participants have suggested looking into theorems that provide necessary and sufficient conditions for canonical transformations. There is no clear consensus on the approach to take, and the conversation includes expressions of frustration regarding the assignment's expectations.

Contextual Notes

Participants note that the problem does not provide additional information or constraints, leading to confusion about the requirements for the solution. There is also mention of the workload and the impact it has on participants' feelings towards the assignment.

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

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