Hilbert-Palatini non-holonomic principle

The Ililbert-Palatini variational principle is considered within the framework of the ADM formalism in a non-holonomic frame of reference. Following Palatiniʹs idea, the more general expression of the action is given with respect to both the arbitrary variation of the metric and to a set of first order independent variables. The equations of the Cauchy problem might be considered as constraints equations together with a further set of constraints arising from the non-holonomic formalism. The Hilbert-Palatini variational principle is obtained for a charged disgregate continuous system.