  The phase space coordinates of individual halo stars obtained by Galactic
surveys enable the computation of their full 3-dimensional orbits. Spectral
analysis of halo orbits can be used to construct "frequency maps" which provide
a compact representation of the 6-dimensional phase space distribution
function. Frequency maps identify important major orbit families, and the
orbital abundances reflect the shape and orientation of the dark matter halo
relative to the disk. We apply spectral analysis to halo orbits in a series of
controlled simulations of disk galaxies. Although the shape of the simulated
halo varies with radius, frequency maps of local samples of halo orbits
confined to the inner halo contain most of the information about the global
shape of the halo and its major orbit families. Quiescent or adiabatic disk
formation results in significant trapping of halo orbits in resonant orbit
families (i.e. orbits with commensurable frequencies). If a good estimate of
the Galactic potential in the inner halo (within ~50kpc) is available, the
appearance of strong, stable resonances in frequency maps of halo orbits will
allow us to determine the degree of resonant trapping induced by the disk
potential. The locations and strengths of these resonant families are
determined both by the global shape of the halo and its distribution function.
Identification of such resonances in the Milky Way's stellar halo would
therefore provide evidence of an extended period of adiabatic disk growth. If
the Galactic potential is not known exactly, a measure of the diffusion rate of
large sample of 10^4 halo orbits can help distinguish between the true
potential and an incorrect potential. The orbital spectral analysis methods
described in this paper provide a strong complementarity to existing methods
for constraining the potential of the Milky Way halo and its stellar
distribution function (ABRIDGED).
