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

by yicong2011
Tags: angular momentum, components, independent
 P: 76 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.
 P: 969 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.
 Sci Advisor P: 3,478 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.

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