1. The problem statement, all variables and given/known data Right I've got a relativistic particle in D dimensional space interacting with a central potential field. Writing out the entire lagrangian is a bit complicated on this but I'm sure you all know the L for a free relativistic particle. The potential term is Ae-br where r is the position vector. (i) Find the momentum p as a function of the velocity v. (ii) Find Lagrange's equations of motion for the particle. (iii) Find the velocity v as a function of P and r. 2. Relevant equations 3. The attempt at a solution (i) That would be mvi/root(1 - v2/c2) (ii) ∂L/∂xi = d/dt(∂L/∂vi) , Pi = ∂L/∂vi So dPi/dt = Abe-brxi/r (iii) This is the part I'm having a problem with. I have that v2 = P2c2/(m2c2 + P2) But I have no idea how to get r into the equation. Advice please?