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The equations of motion of a mechanical system subjected to nonholonomiclinear constraints can be formulated in terms of a linear almost Poissonstructure in a vector bundle. We study the existence of invariant measures forthe system in terms of the unimodularity of this structure. In the presence ofsymmetries, our approach allows us to give necessary and sufficient conditionsfor the existence of an invariant volume, that unify and improve resultsexisting in the literature. We present an algorithm to study the existence of asmooth invariant volume for nonholonomic mechanical systems with symmetry andwe apply it to several concrete mechanical examples.

Unimodularity and preservation of volumes in nonholonomic mechanics