Show that if the potential in the Lagrangian contains-velocity dependent terms, the canonical momentum corresponding to the coordinate of rotation θ, is no longer the mechanical angular momentum but is given by:
p = L - Ʃn[itex]\bullet[/itex]ri x ∇viU
The Attempt at a Solution
Setting: L = T - V(qi,qi')
Lagranges equation must be satisfied***:
d/dt(∂L/∂qi') - ∂L/∂qi = 0
d/dt(∂T/∂qi' - ∂V/∂qi') - ∂V/∂qi = 0
Am I on the right track?
I know I am supposed to use ∂ri/∂qi = nxr somewhere.
** Why is it that it MUST be satisfied?