# The usefulness of the action-angle variables

1. Jan 14, 2010

### wdlang

i am now reading the book by goldstein on classical mechanics

classical mechanics is always a difficult subject for me

as for the action angle variables, i have some questions.

If a system is chaotic, so that a trajectory may never close

in this case, how can we define an action variable. In his book, the actioni s defined along a closed orbit

actually, for an arbitrary central field, the orbit may never close, then in this case, the action can not be defined!

therefore, it seems that the action angle variables can only be defined for some particular system.