  We study the linear stability of a circular orbit in a two-electron atom,
with the inclusion of retardation and self-interaction effects. We calculate
all the eigenvalues of the linear stability of the circular orbit, expanded up
to third order in (v/c). We discuss how the linear stability results can be
used to construct a resonant normal form constant of motion, which is important
for the short time stability of the orbits (e.g. emission of sharp spectral
lines). We calculate the magnitudes related to some of those orbits and compare
to the quantum atomic results.
