  We study singularity formation in spherically symmetric solitons of the
charge one sector of the (2+1) dimensional S^2 sigma model, also known as $\IC
P^1$ wave maps, in the adiabatic limit. These equations are non-integrable, and
so studies are performed numerically on radially symmetric solutions using an
iterative finite differencing scheme. Analytic estimates are made by using an
effective Lagrangian cutoff outside a ball of fixed radius. We show the
geodesic approximation is valid when the cutoff is applied, with the cutoff
approaching infinity linearly as the reciprocal of the initial velocity.
Additionally a characterization of the shape of a time slice f(r,T) with T
fixed is provided.
