  Platform motion poses significant challenges to high-precision optical time
and frequency transfer. We give a detailed description of these challenges and
their solutions in comb-based optical two-way time and frequency transfer
(O-TWTFT). Specifically, we discuss the breakdown in reciprocity due to
relativity and due to asynchronous sampling, the impact of optical and
electrical dispersion, and velocity-dependent transceiver calibration. We
present a detailed derivation of the equations governing comb-based O-TWTFT in
the presence of motion. We describe the implementation of real-time signal
processing algorithms based on these equations and demonstrate active
synchronization of two sites over turbulent air paths to below a femtosecond
time deviation despite effective velocities of +/-25 m/s, which is the maximum
achievable with our physical setup. With the implementation of the time
transfer equation derived here, we find no velocity-dependent bias between the
synchronized clocks to within at two-sigma statistical uncertainty of 330
attoseconds.
