Are Lx, Ly, Lz (the components of Angular Momentum)independent to each other?by yicong2011 Tags: angular momentum, components, independent 

#1
Apr2311, 08:35 PM

P: 76

In Classical Mechanics, are the three components of Angular Momentum L:
L_{x}, L_{y}, L_{z} independent to each other? It seems that there is an identity in Classical 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 LeviCivita Tensor If the identity is true, then the three components of Angular Momentum are not independent to each other. 



#2
Apr2311, 10:41 PM

P: 969

Angular momenta are independent of each other. Take the obvious case of planar motion in the xyplane. Then L_{x} and L_{y} are zero, and L_{z} can be anything.



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