Ruben Martín

Departamento de Matemática Aplicada IV, Universidad Politécnica de Cataluña

Sistemas singulares dependientes del tiempo
The dynamics defined by a singular lagrangian lead to equations of motion of a particular kind, namely, first-order differential equations which are affine on velocities, A(t,x)x' = b(t,x), where A is a singular matrix. One of the objectives of this contribution is to extend the known geometric formulation of the autonomous case to the time-independent case. To this aim, jet bundles must be used. We will also study the obtaining of solutions by means of constraint algorithms, either directly or through an equivalent autonomous system. Anologous results will be obtained for second-order equations. Finally, the formalism will be applied to the study of singular systems arising in mechanics.