What is the meaning of the Jacobi identity for Poisson brackets?

[M. next]

What is the physical meaning of Jacobi identity for Poisson brackets? When does it come in handy?

It goes as follows: {f,{g,h}}+{g,{h,f}}+{h,{f,g}}=0

Thanks.

 

[UltrafastPED]

For the abstract meaning see: http://mathworld.wolfram.com/JacobiIdentities.html
The Poisson brackets are the commutator here, and the system forms a Lie algebra.

Wikipedia goes further: http://en.wikipedia.org/wiki/Jacobi_identity
When this equality is satisfied it tells us something definite about infinitesimal motions ...

A particular application occurs in Hamiltonian mechanics:
http://sci.tech-archive.net/Archive/sci.physics/2004-07/5342.html

 

[M. next]

Thank you!