Can you find two different constants by Noether's theorem

[qinglong.1397]

Homework Statement

Consider a 3-dimensional one-particle system whose potential energy in cylindrical polar coordinates \rho, \theta, z is of the form V(\rho, k\theta+z), where k is a constant.

Homework Equations

The Attempt at a Solution

I already find a symmetric transformation:
\rho '=\rho, \theta '=\theta+\theta_0, z'=z-k\theta_0.

Can you help me find at least another one? Thank you!

 

[qinglong.1397]

No body can do it?

 

[diazona]

For starters, are you sure there is another one?

 

[Hurkyl]

And what have you done on the problem? It is strictly against policy to just hand out answers -- it's cheating and does little to help the student learn.

 

[qinglong.1397]

And what have you done on the problem? It is strictly against policy to just hand out answers -- it's cheating and does little to help the student learn.

I found one solution, as mentioned in the first post. I just do not know how to find the other one. I need your help. Just hint. Thanks!

 

[qinglong.1397]

This is a problem from Classical Dynamics: A contemproray approach by Jose. I think it is not very possible that it is wrong.

 

[diazona]

Ah yes... problem 3.11 by any chance? Now that you mention it, I remember doing that one for a homework assignment once upon a time and I seem to remember having the same difficulty with it.

Try thinking about symmetries in time, since you've already considered the three spatial coordinates.

 

[qinglong.1397]

Ah yes... problem 3.11 by any chance? Now that you mention it, I remember doing that one for a homework assignment once upon a time and I seem to remember having the same difficulty with it.

Try thinking about symmetries in time, since you've already considered the three spatial coordinates.

Oh, yeah. I never thought about that. Thank you very much!