Geometrically, the vector-function (7) implements an embedding of the configuration space M of the constrained Newtonian dynamical system into the 3 N -dimensional flat configuration space of the unconstrained Newtonian dynamical system (3). Due to this embedding the Euclidean structure of the ambient space induces the Riemannian metric onto the manifold M . The components of the metric tensor of this induced metric are given by the formula