  Inspirals of rotating stellar-mass compact objects into massive black holes
are influenced by the spin-curvature coupling, which drives the compact body
away from geodesic motion due to its rotation. I formulate the Hamilton-Jacobi
equation for a spinning test body orbiting a Kerr black hole, solve it to
linear order in spin, and use the perturbative solution to compute the
fundamental frequencies of motion along the orbit. This result provides one of
the necessary ingredients for waveform models for the upcoming space-based
gravitational-wave detector LISA.
