We carry out a set of self-consistent N -body calculations to investigate how important the velocity anisotropy in non-spherical dark-matter halos is for dynamical friction .
For this purpose we allow satellite galaxies to orbit within flattened and live dark-matter haloes ( DMHs ) and compare the resulting orbit evolution with a semi-analytic code .
This code solves the equation of motion of the same satellite orbits with mass loss and assumes the same DMH , but either employs Chandrasekhar ’ s dynamical friction 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 , whereas the parent galaxy is composed of a DMH with aspect ratio q _ { h } = 0.6 .

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 .
Binney ’ s treatment therefore appears to provide a significantly improved treatment of dynamical friction in anisotropic systems .

The velocity anisotropy of the DMH velocity distribution function leads to a significant decrease with time of the inclination of non-polar satellite orbits .
But at the same time it reduces the difference in decay times between polar and coplanar orbits evident in a flattened DMH when the anisotropic DMH velocity distribution function is not taken into account explicitly .
Our N - body calculations furthermore indicate that polar orbits survive about 1.6 times longer than coplanar orbits and that the orbital eccentricity e remains close to its initial value if satellites decay slowly towards the galaxy centre .
However , orbits of rapidly decaying satellites modelled with the semi-analytic code show a strong orbital circularisation ( \dot { e } < 0 ) not present in the N-body computations .