  The dynamics of the spin-orbit interaction in atomic hydrogen are studied in
a classical electrodynamics-like setting. A Rutherfordian atomic model is used
assuming a circular electron orbit, without the quantum principle as imposed
arbitrarily in the Bohr model, but with an ad hoc incorporation in the electron
of intrinsic spin and associated magnetic dipole moment. Analyzing the motions
of the electron spin and orbital angular momenta, it is found that in the
presence of Thomas precession, the total angular momentum averaged over the
orbit is not generally a constant of the motion. It is noted this differs from
the finding of Thomas in a similar assessment of 1927, and the reason for this
difference is provided. It is found that although the total orbit-averaged
angular momentum is not a constant of the motion, it precesses around a fixed
axis similarly to the precession of the total angular momentum vector seen in
spin-orbit coupling in quantum theory. The magnitude of the angular velocity of
the total orbit-averaged angular momentum is seen to vanish only when the spin
and orbital angular momenta are antiparallel and their mutual precession
frequencies equate. It is then found, there is a unique radius where the mutual
precession frequencies equate. Assuming the electron magnetic moment is the
Bohr magneton, and an electron g-factor of two, this radius corresponds to
where the orbital angular momentum is the reduced Planck's constant. The orbit
radius for stationary total angular momentum for the circular orbit model with
nonzero orbital angular momentum is thus the ground-state radius of the Bohr
model.
