  We carry out a set of self-consistent N-body calculations to investigate how
important the velocity anisotropy in non-spherical dark-matter haloes is for
dynamical friction. For this purpose we allow satellite galaxies to orbit
within flattened and live dark-matter haloes (DMHs) with aspect-ratio q_h=0.6
and compare the resulting orbit evolution with a semi-analytic code. This code
solves the equation of motion of satellites orbiting within the same DMH and
implements, according to the dynamical friction model, either Chandrasekhar's
formula, which does not incorporate the velocity anisotropy, or Binney's
description of dynamical friction in anisotropic systems. In the numerical and
the two semi-analytic models the satellites are given different initial orbital
inclinations and orbital eccentricities.
  We find that Binney's approach successfully describes the overall satellite
decay and orbital inclination decrease for the whole set of orbits, with an
averaged discrepancy of less than 4 per cent in orbital radius during the first
3 orbits. If Chandrasekhar's expression is used instead, the discrepancy
increases to 20 per cent and no inclination decrease can be observed. Binney's
treatment therefore appears to provide a significantly improved treatment of
dynamical friction in anisotropic systems.
