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We present a new class of high-order variational integrators on Lie groups.We show that these integrators are symplectic, momentum preserving, and can beconstructed to be of arbitrarily high-order, or can be made to convergegeometrically. Furthermore, these methods are stable and accurate for verylarge time steps. We demonstrate the construction of one such variationalintegrator for the rigid body, and discuss how this construction could begeneralized to other related Lie group problems. We close with severalnumerical examples which demonstrate our claims, and discuss further extensionsof our work.

Lie Group Spectral Variational Integrators