\begin{abstract}
The evolution of the muon spin in the g-2 storage ring is characterized by the Thomas-BMT equation.
The equation gives the time dependence of the orientation of the muon spin on the magnetic and electric fields
and the muon velocity. That interaction can alternatively be described by an effective Hamiltonian, 
and the dynamics by Schrodinger's equation. In the following, an effective Hamiltonian is derived
for the case of vertical oscillations driven by electrostatic focusing (pitching motion), longitudinal magnetic fields,
and radial magnetic fields. The formalism yields exact solutions for the muon precession frequency in the rotating frame in the case of a fixed pitch angle (zero electric field),
and uniform radial and longitudinal fields. The effect of vertical oscillations including electrostatic focusing is
determined perturbatively, as is the effect of non uniform longitudinal fields.
\end{abstract}
