Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Local constants of motion?

  1. Aug 1, 2010 #1
    I don't know if this is the right place to post this, but my question is: if i have an Hamiltonian defined on the whole phase space and a function f which is also defined on the whole phase space and doesn't depend explicitly on time, i know that if its poisson bracket with the Hamiltonian vanishes everywhere, f is a constant of the motion. But what happens if this poisson bracket doesn't vanish everywhere, but only on a subset of the phase space? This subset could be for example the one i get from the equation {f,H}=0

    Thanks!
     
  2. jcsd
  3. Aug 6, 2010 #2
    Welcome giova7_89,
    If the locus of {f,H}=0 contains a trajectory, f will indeed be constant for that trajectory. If one considers the analytic continuation, one must say that such local constants have little physical significance.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook