Brachistochrone Problem with Coulomb Friction and Viscous Drag: Qualitative Analysis

摘要

The range maximization problem and corresponding the brachistochrone problem with Coulomb and viscous friction are considered. A maximum principle procedure allows to reduce optimal control problem to the boundary-value problem for a system of two non-linear differential equations. Solution of this system is corresponding to the motion under singular control. Qualitative analysis of the trajectories is carried out, typical features are determined and verified by means of numerical simulation.