1. Sep 25, 2013 #1

   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.

    

   M. next, Sep 25, 2013
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3. Sep 25, 2013 #2

   UltrafastPED

   

   Science Advisor

   Gold Member

   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

    

   UltrafastPED, Sep 25, 2013
4. Sep 26, 2013 #3

   M. next

   

   Thank you!

    

   M. next, Sep 26, 2013

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