  In this paper, high-order numerical integrators on homogeneous spaces will be
presented as an application of nonholonomic partitioned Runge-Kutta Munthe-Kaas
(RKMK) methods on Lie groups.
  A homogeneous space $M$ is a manifold where a group $G$ acts transitively.
Such a space can be understood as a quotient $M \cong G/H$, where $H$ a closed
Lie subgroup, is the isotropy group of each point of $M$. The Lie algebra of
$G$ may be decomposed into $\mathfrak{g} = \mathfrak{m} \oplus \mathfrak{h}$,
where $\mathfrak{h}$ is the subalgebra that generates $H$ and $\mathfrak{m}$ is
a subspace. Thus, variational problems on $M$ can be treated as
nonholonomically constrained problems on $G$, by requiring variations to remain
on $\mathfrak{m}$.
  Nonholonomic partitioned RKMK integrators are derived as a modification of
those obtained by a discrete variational principle on Lie groups, and can be
interpreted as obeying a discrete Chetaev principle. These integrators tend to
preserve several properties of their purely variational counterparts.
