Hi, I tried to solve this problem, but I was unsuccessful :grumpy:(adsbygoogle = window.adsbygoogle || []).push({});

Here is the problem:

Given the transformation:

[itex] \left \{ \begin{array}{l} Q = p^\gamma \cos(\beta q) \\ P = p^\alpha \sin(\beta q) \end{array} \right. [/itex]

a) Determine the values of the constants [itex] \alpha [/itex], [itex] \beta [/itex] and [itex] \gamma [/itex] for which this transformation is canonical.

b) In correspondence of these values, find a generating function of the transformation.

How can I solve this problem? Firstly, I used the Poisson bracket condition for canonicity:

[itex] [Q,P]_{q,p} = \frac{\partial Q}{\partial q}\frac{\partial P}{\partial p}-\frac{\partial Q}{\partial p}\frac{\partial P}{\partial q} [/itex].

Afterwards I supposed:

[itex] pdq-PdQ [/itex]

to be an exact differential.

Still, I didn't manage to find [itex] \alpha [/itex], [itex] \beta [/itex] and [itex] \gamma [/itex], as if I missed a condition...

Can you help me, please?

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# Canonical Transformation

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