Pewne uogólnienie problemu brachistochrony

In this paper a certain generalization is given of the brachistochrone problem by introducing the slide friction. The problem is reduced to the system (23) of three non-linear, ordinary differential equations. The exact solution of these equations is not possible but an approximate solution may be obtained, for example by means of the iteration method. In the paper also the formula (17) is qiven for the determination of the time of fall of the material point along an arbitrary curve lying in the vertical plane, the slide friction being taken into account. The differential equation (32) describing the curve on which the velocity of the material point is constant has been additionally obtained.