Abstract
The horizontal coordinate maximization problem of a mass-point as well as the corresponding brachistochrone problem is considered. The mass-point is assumed to be moving in a vertical plane under the influence of gravity and viscous drag that is proportional to the nth degree of the velocity. An analysis of the reaction force, which is considered as control along the extremal curve, is provided. It is established that the reaction of the basement can change its sign no more than one time, moreover; it changes only from negative values to positive values.
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