Register to reply

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

by yicong2011
Tags: angular momentum, components, independent
Share this thread:
Apr23-11, 08:35 PM
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.
Phys.Org News Partner Physics news on
Step lightly: All-optical transistor triggered by single photon promises advances in quantum applications
The unifying framework of symmetry reveals properties of a broad range of physical systems
What time is it in the universe?
Apr23-11, 10:41 PM
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.
Apr24-11, 03:49 PM
Sci Advisor
Bill_K's Avatar
P: 4,160
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.

Register to reply

Related Discussions
Counting independent components Special & General Relativity 1
Independent Components in Riemann-Christoffel Tensor Special & General Relativity 3
Components for the angular momentum operator L Advanced Physics Homework 4
Independent components of tensor Calculus & Beyond Homework 1
How many independent components Classical Physics 17