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Several scenarios have been proposed in which the orbits of binary blackholes enter the band of a gravitational wave detector with significanteccentricity. To avoid missing these signals or biasing parameter estimation itis important that we consider waveform models that account for eccentricity.The ingredients needed to compute post-Newtonian (PN) waveforms produced byspinning black holes inspiralling on quasi-eccentric orbits have been availablefor almost two decades at 2 PN order, and this work has recently been extendedto 2.5 PN order. However, the computational cost of directly implementing thesewaveforms is high, requiring many steps per orbit to evolve the system ofcoupled differential equations. Here we employ the standard techniques of aseparation of timescales and a generalized Keplerian parameterization of theorbits to produce efficient waveforms describing spinning black hole binarieswith arbitrary masses and spins on quasi-eccentric orbits to 1.5 PN order. Weseparate the fast orbital timescale from the slow spin-orbit precessiontimescale by solving for the orbital motion in a non-interial frame ofreference that follows the orbital precession. We outline a scheme forextending our approach to higher post-Newtonian order.Comment: 11 pages, introduction and references update

Computing waveforms for spinning compact binaries in quasi-eccentric orbits