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

Are Lx, Ly, Lz (the components of Angular Momentum)independent to each other?

  1. Apr 23, 2011 #1
    In Classical Mechanics, are the three components of Angular Momentum L:

    Lx, Ly, Lz

    independent to each other?

    It seems that there is an identity in Classical Mechanics (Sorry, I can hardly remember where I saw it):

    [Li, Lj] = εijk Lk.

    Note: [] is Poisson Bracket, εijk is Levi-Civita Tensor

    If the identity is true, then the three components of Angular Momentum are not independent to each other.
     
  2. jcsd
  3. Apr 23, 2011 #2
    Angular momenta are independent of each other. Take the obvious case of planar motion in the xy-plane. Then Lx and Ly are zero, and Lz can be anything.
     
  4. Apr 24, 2011 #3

    Bill_K

    User Avatar
    Science Advisor

    yicong, Of course you are misinterpreting the meaning of the Poisson bracket. Note for example in three dimensions with Cartesian coordinates xi, the Poisson bracket relationship [xi, xj] = 0 for i and j not equal.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Are Lx, Ly, Lz (the components of Angular Momentum)independent to each other?
  1. Angular Momentum (Replies: 1)

  2. Angular momentum (Replies: 1)

Loading...