# Lagrangian and symmetry

1. Sep 7, 2014

### noor

1. The problem statement, all variables and given/known data

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)

2. Relevant equations

k is constant
L=T-V
T is kinetic energy
3. The attempt at a solution
i tried to find translational symmetry
r --> r+s
theta --> theta-s/k
im not sure any help please ?

2. Sep 8, 2014

### 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!