  This paper presents a theoretical study of oscillatory and rotational
instabilities of a solid spherical body, levitated electromagnetically in
axisymmetric coils made of coaxial circular loops. We apply our previous theory
to analyze the static and dynamic stability of the sample depending on the ac
frequency and the position of the sample in the coils for several simple
configurations. We introduce an original analytical approach employing a gauge
transformation for the vector potential. First, we calculate the spring
constants that define the frequency of small-amplitude oscillations. For static
stability, the spring constants must be positive. Dynamic instabilities are
characterized by critical ac frequencies that, when exceeded, may result either
in a spin-up or oscillations with increasing amplitude. We found that the
critical frequencies increase with the nonuniformity of the field. We show that
for a spherically harmonic field, the critical frequency for the spin-up
instability in a field of degree $l$ coincides with the critical frequency for
the oscillatory instability in a field of degree $l+1$.
