  The simulation of systems that act on multiple time scales is challenging. A
stable integration of the fast dynamics requires a highly accurate
approximation whereas for the simulation of the slow part, a coarser
approximation is accurate enough. With regard to the general goals of any
numerical method, high accuracy and low computational costs, a popular approach
is to treat the slow and the fast part of a system differently. Embedding this
approach in a variational framework is the keystone of this work. By
paralleling continuous and discrete variational multirate dynamics, integrators
are derived on a time grid consisting of macro and micro time nodes that are
symplectic, momentum preserving and also exhibit good energy behaviour. The
choice of the discrete approximations for the action determines the convergence
order of the scheme as well as its implicit or explicit nature for the
different parts of the multirate system. The convergence order is proven using
the theory of variational error analysis. The performance of the multirate
variational integrators is demonstrated by means of several examples.
