CONSTRAINED SYSTEMS - A UNIFIED GEOMETRIC APPROACH

A general geometric framework is devised in order to contain the presymplectic and Lagrangian formalisms as particular cases. We call these objects constrained dynamical system, since their dynamics usually lead to constraints. Their most elementary properties are studied, and several related structures, especially morphisms, are defined. In particular, a stabilization algorithm is performed. As a byproduct, the dynamics and constraints of the Lagrangian formalism (with the "second-order condition") are intrinsically obtained.