naa a22 4500 510809936 CHVBK 20180411083438.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1134/S1064230713040084 doi (NATIONALLICENCE)springer-10.1134/S1064230713040084 Golubev Yu Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, 125047, Moscow, Russia aut Brachistochrone for a rigid body sliding down a curve [Elektronische Daten] [Yu. Golubev] Extremality conditions in the brachistochrone problem for a perfectly rigid body sliding without friction down an unknown (to be determined) curve in a vertical plane are found. In this case, the body has to track the tangent to the trajectory. According to the principle of constraint release, the reaction of the support creates a torque used as control. For dimensionless Appell's equations with a single similarity coefficient, the standard problem of the fastest descent from a given initial point to a given terminal point assuming that the initial velocity is zero is formulated. The Okhotsimskii-Pontryagin method is used to analyze the differential of the objective function. Necessary optimality conditions are found, and a formula for the optimal control that does not involve adjoint variables is derived from them. Properties of the optimal trajectories are investigated analytically both in the general case and for the limiting (zero and infinite) values of the similarity coefficient. It is found that cycloid-shaped brachistochrones occur as the similarity coefficient tends to infinity. For some values of the similarity coefficient, numerical results are presented that demonstrate the shape of the corresponding brachistochrones and the optimal time of motion. The results are compared with those obtained by solving the classical brachistochrone problem. Pleiades Publishing, Ltd., 2013 Journal of Computer and Systems Sciences International Springer US; http://www.springer-ny.com 52/4(2013-07-01), 571-587 1064-2307 52:4<571 2013 52 11488 https://doi.org/10.1134/S1064230713040084 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S1064230713040084 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Golubev Yu Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, 125047, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Computer and Systems Sciences International Springer US; http://www.springer-ny.com 52/4(2013-07-01), 571-587 1064-2307 52:4<571 2013 52 11488 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer