Lagrangian system of order s ? 1; system of k nonholonomic constraints of order s ? 1; canonical distribution; constraint ideal; nonholonomic constraint structure; constraint Lepage one form; constraint first variational formula

A geometric setting for higher order mechanical systems subjected to nonholonomic constraints of an arbitrary order has been proposed in Ref. 1. In this paper we study the simplest case, when nonholonomic constraints are of order s ? 1, s ? 2, i.e. are given on the dynamical space Js?1Y, where the unconstrained dynamics proceeds. Analogously as in the case of first order constraints we introduce a constraint Lepage form, which provides the invariant decomposition of the Lie derivative into a ?constraint? Euler-Lagrange term and a boundary term. Coordinate expression of the constraint Lepage one form associated with a nonholonomic constraint structure of order s ? 1 is presented, corresponding constraint Euler-Lagrange equations for ?constraint extremals? are obtained.