Editing Poisson bracket (section)

==Properties==
Given two functions {{mvar|f}} and {{mvar|g}} that depend on [[phase space]] and time, their Poisson bracket <math>\{f, g\}</math> is another function that depends on phase space and time. The following rules hold for any three functions <math>f,\, g,\, h</math> of phase space and time:
;[[Anticommutativity]]: <math>\{f, g\} = -\{g, f\}</math>
;[[Bilinearity]]: <math>\{af + bg, h\} = a\{f, h\} + b\{g, h\}, </math><math> \{h, af + bg\} = a\{h, f\} + b\{h, g\}, \quad a, b \in \mathbb R</math>
;[[Product rule|Leibniz's rule]]: <math>\{fg, h\} = \{f, h\}g + f\{g, h\}</math>
;[[Jacobi identity]]: <math>\{f, \{g, h\}\} + \{g, \{h, f\}\} +  \{h, \{f, g\}\} = 0</math>

Also, if a function <math>k</math> is constant over phase space (but may depend on time), then <math>\{f,\, k\} = 0</math> for any <math>f</math>.