Non-Involutive Constrained Systems and Hamilton-Jacobi Formalism
  In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the integrability conditions leads to the reduction of degrees of freedom of these systems and, as consequence, naturally defines a dynamics in a reduced phase space. 
M. C. Bertin, B. M. Pimentel, C. E. Valc\'arcel