Oleg Zubelevich
On the Brachistochrone Problem
(326K, pdf)

ABSTRACT.  In this article we consider different generalizations of the Brachistochrone Problem in the context of fundamental concepts of classical mechanics. 
The correct statement for the Brachistochrone problem for nonholonomic systems is proposed. 
It is shown that the Brachistochrone problem is closely related to vakonomic mechanics.