Brachistochronic motion of nonholonomic nonlinear mechanical system of the Chaplygin type

In this paper, the differential equations of brachistochronic motion of nonholonomic nonlinear system of the Chaplygin type were determined. The additional forces Rα realizing the corresponding motion of the system together with the given forces were also determined. Lastly, the brachistochrone was solved for a concrete model using mathematical numerical methods.