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The title pretty much says it. Say you have a very simple 3D Lagrangian:

[itex]L = \frac{1}{2}m(\dot{x}^2 + \dot{y}^2 + \dot{z}^2) - V[/itex]

So How do you tell what is conserved from a generic potential?

I know for example that if V = V(x,y,z) then the total linear momentum is not conserved, if V = V(x,y) then the z component of linear momentum is conserved...etc.

I get stuck when angular momentum gets involved. For example, what is conserved if [itex]V = V(x^2+y^2, z) [/itex]...I need to know how to spot the conserved quantities generally. I know that the total energy is conserved unless there is explicit dependence on time, so dont worry about that one...im looking for conservation with respect to angular / linear momentum components.

Can you guys help me out please? thanks!