Two-body problems—A unified, classical, and simple treatment of spin-orbit effects

We show how the spin-orbit contribution to the two-body Hamiltonian, to order $c^{-2\mathrm{}}$, may be derived classically, in a simple but rigorous manner, from a knowledge of just the corresponding contributions for the one-body problem. As an illustration of the generality of our results, we consider, as particular cases, the electromagnetic and gravitational interactions and demonstrate how the usual results follow directly.