Hamilton-Jacobi theory for degenerate Lagrangian systems with holonomic and nonholonomic constraints (Q2865541)

The paper deals with Lagrange-Dirac (or implicit Lagrangian) systems - a Lagrangian mechanics which includes degenerate Lagrangians as well as holonomic and nonholonomic constraints, following \textit{H. Yoshimura} and \textit{J. E. Marsden} [J. Geom. Phys. 57, No. 1, 133--156 (2006; Zbl 1107.53053), J. Geom. Phys. 57, No. 1, 209--250 (2006; Zbl 1121.53057)].NEWLINENEWLINEThe paper develops a Hamilton-Jacobi theory for this type of system, defining the Dirac-Hamilton-Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the theory specializes to the nonholonomic Hamilton-Jacobi theory given in [\textit{D. Iglesias-Ponte, M. de León} and \textit{D. Martín de Diego}, J. Phys. A, Math. Theor. 41, No. 1, 015205, 14 p. (2008; Zbl 1154.70007)].NEWLINENEWLINEIn particular, a class of degenerate nonholonomic Lagrangian systems with symmetries - weakly degenerate Chaplygin systems, is studied. It is shown that these systems, similarly as usual G-Chaplygin systems, reduce to non-degenerate almost Hamiltonian systems. The Dirac-Hamilton-Jacobi equation reduces to a variant of the nonholonomic Hamilton-Jacobi equation associated with the reduced system.