  We study the exchange constants of MnV$_2$O$_4$ using magnetic force theorem
and local spin density approximation of density functional theory supplemented
with a correction due to on-site Hubbard interaction U. We obtain the exchanges
for three different orbital orderings of the Vanadium atoms of the spinel. We
then map the exchange constants to a Heisenberg model with single-ion
anisotropy and solve for the spin-wave excitations in the non-collinear, low
temperature phase of the spinel. The single-ion anisotropy parameters are
obtained from an atomic multiplet exact-diagonalization program, taking into
effect the crystal-field splitting and the spin-orbit coupling. We find good
agreement between the spin waves of one of our orbital ordered setups with
previously reported experimental spin waves as determined by neutron
scattering. We can therefore determine the correct orbital order from various
proposals that exist in the literature.
