In Classical Mechanics, are the three components of Angular Momentum(adsbygoogle = window.adsbygoogle || []).push({}); :L

L_{x},L_{y},L_{z}

independent to each other?

It seems that there is anidentityinClassical Mechanics(Sorry, I can hardly remember where I saw it):

[L_{i},L_{j}] =ε_{ijk}L_{k}.

Note: [] is Poisson Bracket,ε_{ijk}is Levi-Civita Tensor

If theidentityis true, then the three components of Angular Momentum are not independent to each other.

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

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