NDLI: Optimal trajectories in brachistochrone problem with Coulomb friction

Content Provider	Springer Nature Link
Author	Vondrukhov, A. S. Golubev, Yu. F.
Copyright Year	2016
Abstract	A two-parameter family of optimal curves in the brachistochrone problem in the case of Coulomb friction is found. The problem is represented in the form of the standard time minimization control problem. The normal component of the support reaction is used as control. It turned out that the formula for the optimal control, which does not include adjoint variables, has a singularity at the zero motion velocity. A system of ordinary differential equations is derived for which the solution of the Cauchy initial value problem makes it possible to obtain optimal trajectories that have a vertical tangent at the initial point. The self-similarity property of such trajectories is proved. It is shown how this property can be used to obtain by scaling all optimal trajectories from the set of optimal trajectories with fixed initial conditions and different terminal slope angles of the tangent.
Starting Page	341
Ending Page	348
Page Count	8
File Format	PDF
ISSN	10642307
Journal	Journal of Computer and Systems Sciences International
Volume Number	55
Issue Number	3
e-ISSN	15556530
Language	English
Publisher	Pleiades Publishing
Publisher Date	2016-06-30
Publisher Place	Moscow
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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