NDLI: Brachistochrone for a rigid body sliding down a curve

Content Provider	Springer Nature Link
Author	Golubev, Yu. F.
Copyright Year	2013
Abstract	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.
Starting Page	571
Ending Page	587
Page Count	17
File Format	PDF
ISSN	10642307
Journal	Journal of Computer and Systems Sciences International
Volume Number	52
Issue Number	4
e-ISSN	15556530
Language	English
Publisher	Springer US
Publisher Date	2013-08-08
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Control, Robotics, Mechatronics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Computer Networks and Communications Control and Systems Engineering Information Systems Computer Vision and Pattern Recognition Software

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