Lagrange’s equations — UPSC Physics Optional CSE 2004 Paper I

A particle moves in space with the Lagrangian L = \frac{1}{2} m (\dot{x}^2 + \dot{y}^2 + \dot{z}^2) - V + A \dot{x} + B \dot{y} + C \dot{z} where A, B, C are given functions of x, y, z. Find the corresponding Hamiltonian in terms of coordinates and momenta.