  Using N-body simulations we study the phenomenon of radial orbit instability
occurring in dark matter haloes of the size of a dwarf galaxy. We carried out
simulations of seven spherical models, with the same standard NFW density
profile but different anisotropy profiles of particle orbits. Four of them
underwent instability: two with a constant positive anisotropy, one with an
anisotropic core and an isotropic envelope and one with a very small isotropic
core and an anisotropic envelope. Haloes affected by the instability become
approximately axisymmetric and prolate, with the profile of the
shortest-to-longest axis ratio increasing with radius. The lower limit for the
central value of this axis ratio is 0.3 for an NFW halo. The density profiles
of the haloes did not change significantly, whereas the velocity distributions
became axisymmetric. The total angular momentum rose due to large-amplitude
oscillations of its components perpendicular to the symmetry axis of the halo.
We also studied orbits of individual particles assigning them to classical
orbit families in triaxial potentials. We find that the membership of a given
particle in a family depends on its initial total angular momentum and its
components along the principal axes of matter distribution.
