Precisely computing bound orbits of spinning bodies around black holes

Very large mass-ratio binary black hole systems are of interest as a clean limit of the two-body problem in general relativity, as well as for describing important low-frequency gravitational wave (GW) sources. At lowest order, the smaller black hole follows a geodesic of the larger black hole's spacetime. Accurate models of large mass-ratio systems include post-geodesic corrections which account for forces driving the small body away from the geodesic. Spin-curvature forces, which arise due to the coupling of a test body's spin to the spacetime curvature, is an example of such an effect. In a previous talk, we outlined a frequency-domain method for precisely computing bound orbits of spinning test bodies experiencing spin-curvature forces. In this talk, we show how to apply this approach to the fully generic case, in which orbits are inclined and eccentric and with the small body's spin arbitrarily oriented. An osculating geodesic integrator that includes both spin-curvature forces and the backreaction due to GWs can be used to generate an adiabatic spinning-body inspiral. We present preliminary results combining the osculating element description with the tetrad formulation for Kerr parallel transport to build a framework for completely generic worldlines of spinning bodies.