What Does Skew Symmetry Imply for One-Dimensional Systems?

[hoddy]

TL;DR

if I have a equation like (just a random eq.) p_dot = S(omega)*p. where p = [x, y, z] is the original states, omega = [p, q, r] and S - skew symmetric. How does the equation appear if i only want a system to have the state z?

Hi,

if I have a equation like (just a random eq.) p_dot = S(omega)*p. where p = [x, y, z] is the original states, omega = [p, q, r] and S - skew symmetric.
How does the equation appear if i only want a system to have the state z? do I get z_dot = -q*x + p*y. Or is the symmetric not valid so I simply get z_dot = z? or something else?
and the same for rotation matrix? : p_dot = R(omega)*p

Thanks for any replies!

 

[berkeman]

(just a random eq.)

You are asking us to decode a random equation that you made up?

And it would help if you would please learn to post math equations using LaTeX. That would make your postings a lot more clear (well, maybe not if you keep posting random equations...).

The PF LaTeX tutorial is available in the Help pages, under INFO at the top of the page.

 

[hoddy]

Hi berkeman. sorry, here is the complete equation with v, omega, f and g beeing 3x1 vectors:

Im just curious about the first term with the skew symmetric, how it will turn out when I only have it in 1 dimension, like described in original post.

 

[fresh_42]

What should skew symmetry mean in one dimension? S=0? I suspect from your question that we speak about quantum physics, and the three dimensional skew symmetric matrices form a semisimple Lie algebra. It's no longer semisimple in the one dimensional case which is crucial, skew symmetric or not, hence irrelevant in the context you hinted at.