MathLivePoisson bracket
The Poisson bracket of two functions on phase space in canonical coordinates, built from their partial derivatives with respect to positions and momenta. It is used in Hamiltonian mechanics to compute time evolution of observables and to express conserved quantities.
\{f,g\}=\sum_{i=1}^n\left(\frac{\partial f}{\partial q^i}\frac{\partial g}{\partial p_i}-\frac{\partial g}{\partial q^i}\frac{\partial f}{\partial p_i}\right)What the symbols mean
| smooth functions (scalar fields) on phase space | |
| generalized position coordinates | |
| conjugate generalized momenta | |
| number of degrees of freedom |
About this formula
- FieldPhysics
- TopicHamiltonian mechanics
- LevelUniversity
- Also calledPoisson bracket formula, canonical Poisson bracket, Poisson bracket in canonical coordinates, symplectic Poisson bracket, Poisson bracket q p, Poisson bracket definition
- SourceWikidata Q1052775
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