Maximizing Symmetry in Lagrangian for a Particle in 3D Cylindrical Coordinates

[noor]

Homework Statement

the question is that there is a particle in 3 spatial Euclidean dimensions in cylindrical coordinates.
I want to find a symmetry for the lagrangian if the potential energy is function of r and k.theta+z
V=V(r,k.theta+z)

Homework Equations

k is constant
L=T-V
T is kinetic energy

The Attempt at a Solution

i tried to find translational symmetry
r --> r+s
theta --> theta-s/k
im not sure any help please ?

 

[vanhees71]

I'm not through with checking this example, but it looks as if it could be a good idea to use
r, \theta, and
u=k \theta + z
as the generalized variables and then perform the Lagrangeformalism. It's easy to see that with this choice of variables you make use of the very symmetry you've already identified!