Gravitational Waveforms for Precessing, Quasi-circular Binaries via
  Multiple Scale Analysis and Uniform Asymptotics: The Near Spin Alignment Case
  We calculate analytical gravitational waveforms in the time- and
frequency-domain for precessing quasi-circular binaries with spins of arbitrary
magnitude, but nearly aligned with the orbital angular momentum. We first
derive an analytical solution to the precession equations by expanding in the
misalignment angle and using multiple scale analysis to separate timescales. We
then use uniform asymptotic expansions to analytically Fourier transform the
time-domain waveform, thus extending the stationary-phase approximation, which
fails when precession is present. The resulting frequency-domain waveform
family has a high overlap with numerical waveforms obtained by direct
integration of the post-Newtonian equations of motion and discrete Fourier
transformations. Such a waveform family lays the foundations for the accurate
inclusion of spin precession effects in analytical gravitational waveforms, and
thus, it can aid in the detection and parameter estimation of gravitational
wave signals from the inspiral phase of precessing binary systems.
