A historical review on nonholomic mechanics

The aim of this paper is to present a short historical/scientific review on nonholonomic mechanics, with special emphasis on the latest developments. Indeed, the use of differential geometric tools has permitted in the last 25 years a fast and unsuspected advance in the theory, particularly in a better understanding of symmetries and reduction, Hamilton–Jacobi theory and integrability characterizations, and the construction of suitable geometric integrators. The last part of the paper is devoted to discuss the latest results in Hamilton–Jacobi theory for nonholonomic dynamics using our own approach.