  Waveform models are essential for gravitational-wave (GW) detection and
parameter estimation of coalescing compact-object binaries. More accurate
models are required for the increasing sensitivity of current and future GW
detectors. The effective-one-body (EOB) formalism combines the post-Newtonian
(PN) and small mass-ratio approximations with numerical-relativity results, and
produces highly accurate inspiral-merger-ringdown waveforms. In this paper, we
derive the analytical precessing-spin two-body dynamics for the SEOBNRv5
waveform model, which has been developed for the upcoming LIGO-Virgo-KAGRA
observing run. We obtain an EOB Hamiltonian that reduces to the exact Kerr
Hamiltonian in the test-mass limit. It includes the full 4PN precessing-spin
information, and is valid for generic compact objects (i.e., for black holes or
neutron stars). We also build an efficient and accurate EOB Hamiltonian that
includes partial precessional effects, notably orbit-averaged in-plane spin
effects for circular orbits, and derive 4PN-expanded precessing-spin equations
of motion, consistent with such an EOB Hamiltonian. The results were used to
build the computationally-efficient precessing-spin multipolar SEOBNRv5PHM
waveform model.
