  We consider the motion of a point particle in a stationary spacetime under
the influence of a scalar, electromagnetic or gravitational self-force. We show
that the conservative piece of the first-order self-force gives rise to
Hamiltonian dynamics, and we derive an explicit expression for the Hamiltonian
on phase space. Specialized to the Kerr spacetime, our result generalizes the
Hamiltonian function previously obtained by Fujita et. al., which is valid only
for non-resonant orbits. We discuss implications for the first law of binary
black hole mechanics.
