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In this paper, high-order numerical integrators on homogeneous spaces will bepresented 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 closedLie 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 $\mathfrak{m}$ isa subspace. Thus, variational problems on $M$ can be treated asnonholonomically constrained problems on $G$, by requiring variations to remainon $\mathfrak{m}$.  Nonholonomic partitioned RKMK integrators are derived as a modification ofthose obtained by a discrete variational principle on Lie groups, and can beinterpreted as obeying a discrete Chetaev principle. These integrators tend topreserve several properties of their purely variational counterparts.

High-order integrators for Lagrangian systems on homogeneous spaces via nonholonomic mechanics