Mathematical Physics: Classical Mechanics by Andreas Knauf

Author:Andreas Knauf
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

To find action coordinates associated with the angles , we are looking for a property of the mapping

that determines for I to be appropriate. I only depends on the values of F, so , with . Since , the will also Poisson-commute.

The derivative is determined by the intended values of the Poisson brackets. The first argument of in (13.3.4) is equal to . So using the dual basis vectors , , it follows that . Finally, from

(13.3.5)

it follows that

or . As the basis vectors are constant on the tori, and can therefore be written as , the determining equation is simply

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