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Understanding the orbits of spinning bodies in curved spacetime is importantfor modeling binary black hole systems with small mass ratios. At zeroth orderin mass ratio, the smaller body moves on a geodesic. Post-geodesic effects areneeded to model the system accurately. One very important post-geodesic effectis the gravitational self-force, which describes the small body's interactionwith its own contribution to a binary's spacetime. Another post-geodesiceffect, the spin-curvature force, is due to the smaller body's spin coupling tospacetime curvature. In this paper, we combine the leading orbit-averagedbackreaction of point-particle gravitational-wave emission with thespin-curvature force to construct the worldline and gravitational waveform fora spinning body spiraling into a Kerr black hole. We use an osculating geodesicintegrator, which treats the worldline as evolution through a sequence ofgeodesic orbits, as well as near-identity transformations, which eliminatedependence on orbital phases, allowing for fast computation of inspirals. Theresulting inspirals and waveforms include all critical dynamical effects whichgovern such systems (orbit and precession frequencies, inspiral, strong-fieldgravitational-wave amplitudes), and as such form an effective first model forthe inspiral of spinning bodies into Kerr black holes. We emphasize that ourpresent calculation is not self consistent, since we neglect effects whichenter at the same order as effects we include. However, our analysisdemonstrates that the impact of spin-curvature forces can be incorporated intoEMRI waveform tools with relative ease. The calculation is sufficiently modularthat it should not be difficult to include neglected post-geodesic effects asefficient tools for computing them become available. (Abridged)

Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations