A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value

• Published in: International journal of non-linear mechanics 2018-05, Vol.101, p.26-35
• Main Authors: Radulović, Radoslav, Jeremić, Bojan, Šalinić, Slaviša, Obradović, Aleksandar, Dražić, Milan
• Format: Article
• Language: English
• Subjects: Brachistochrone; Control theory; Global minimum time; Mathematics; Optimal control; Optimization; Singular control; Symmetry
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2018.02.001

We consider the brachistochrone problem of the particle with a preselected interval for the normal reaction force value as well as the terminal position of the particle lying on an arbitrary planar curve. We use optimal control theory to solve the formulated brachistochrone problem. Here we treat the brachistochrone curve as a bilateral ideal constraint. We study the cases of symmetrically and unsymmetrically preselected intervals for the normal reaction force value. We show that in the case of a symmetrically preselected interval for the normal reaction force value, the brachistochrone curve is a two-segment curve, and in the case of an unsymmetrically preselected interval, it is a three-segment curve. We present a numerical procedure for the identification of the global minimum time of motion. Finally, we present several examples to illustrate the approach proposed in the paper. •The brachistochrone problem with preselected interval for the normal reaction force value is solved.•The cases of symmetrically and unsymmetrically preselected interval for the normal reaction force value are considered.•A numerical procedure for the identification of the global minimum time of motion is presented.