The non-holonomic Herglotz problem dealt with in mechanical terms. Addendum: “The non-holonomic Herglotz variational problem” [J. Math. Phys. 65, 000000 (2024)]

The geometric setup for the study of the non-holonomic Herglotz problem is extended to the case of mechanical kinetic constraints, meant as constraints interacting with the system through corresponding reactive forces. All constraints are assumed to be ideal. Three possible approaches to the determination of the extremals are considered: the direct use of a non-holonomic counterpart of the Lagrange–d’Alembert principle; a formulation à la Poincaré-Cartan, based on the introduction of a suitable differential ideal; an adaptation of the super-lagrangian formalism.