Let (Q,g) be the configuration space of a nonholonomic mechanical system, where g is a Riemannian metric on Q. Suppose the horizontal distribution D on Q admits a vertical distribution D, that is D is an integrable complementary (not necessarily orthogonal) distribution to D in TQ. We prove the existence and uniqueness of a linear connection on (Q,g) subject to some conditions on its torsion and on the covariant derivative of g. Then we show that the solutions of the Lagrange-d'Alembert equations are the geodesics of del and vice versa. All the local components of the torsion and curvature tensor fields of del with respect to an adapted frame field are determined. Finally, two examples are given to illustrate the theory we develop in the paper. (c) 2007 American Institute of Physics.
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