Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was wondering whether it is correct to say that if two components of the angular momentum are conserved, then all three Cartesian coordinates of the angular momentum are conserved? I would regard this as a direct consequence from the Poisson bracket. Is this correct so far?

share|cite|improve this question
up vote 7 down vote accepted

Yes, because $\{J_i,J_j\}_{PB}=\sum_{k=1}^3\epsilon_{ijk} J_k$. More generally, the statement that the Poisson bracket of any two constants of motion is again a constant of motion is known as Poisson's Theorem.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.