We carry out a set of self-consistent N -body calculations to compare the decay rates of satellite dwarf galaxies orbiting a disc galaxy embedded in a dark matter halo ( DMH ) .
We consider both spherical and oblate axisymmetric DMHs of aspect ratio q _ { h } = 0.6 .
The satellites are given different initial orbital inclinations , orbital periods and mass .
The live flattened DMHs with embedded discs and bulges are set-up using a new fast algorithm , MaGalie ( Boily , Kroupa & Peñarrubia 2001 ) .

We find that the range of survival times of satellites within a flattened DMH becomes \sim 100 \% larger than the same satellites within a spherical DMH .
In the oblate DMH , satellites on polar orbits have the longest survival time , whereas satellites on coplanar prograde orbits are destroyed most rapidly .
The orbital plane of a satellite tilts as a result of anisotropic dynamical friction , causing the satellite ’ s orbit to align with the plane of symmetry of the DMH .
Polar orbits are not subjected to alignment .
Therefore the decay of a satellites in an axisymmetric DMH may provide a natural explanation for the observed lack of satellites within 0 - 30 ^ { \circ } of their host galaxy ’ s disc ( Holmberg 1969 ; Zaritsky & González 1999 ) .

The computations furthermore indicate that the evolution of the orbital eccentricity e is highly dependent of its initial value e ( t = 0 ) and the DMH ’ s shape .
We also discuss some implications of flattened DMHs for satellite debris streams .