Poisson Bracket - Canonical Coordinates

Canonical Coordinates

In canonical coordinates (also known as Darboux coordinates) on the phase space, given two functions and, the Poisson bracket takes the form

\{f,g\} = \sum_{i=1}^{N} \left[ \frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} - \frac{\partial f}{\partial p_{i}} \frac{\partial g}{\partial q_{i}} \right].

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