LAGRANGIAN THEORY FOR PRESYMPLECTIC SYSTEMS

We analyze the lagrangian formalism for singular lagrangian systems in a geometrical way. In particular, the problem of finding a submanifold of the velocity phase space and a tangent vector field which is a solution of the lagrangian equations of motion and a second order differential equation (SODE) is studied. Thus, we develop, in a pure lagrangian context, an algorithm which solves simultaneously the problem of the compatibility of the equations of motion, the consistency of their solutions and the SODE problem. This algorithm allows to construct these solutions and gives all the lagrangian constraints, splitting them into two kinds. In this way, previous works on the same subject are completed and improved.