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Optimal Trajectories in Brachistochrone Problem with Coulomb Frictionстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 26 сентября 2016 г.
- Авторы: Vondrukhov A.S., Golubev Yu F.
- Журнал: Journal of Computer and Systems Sciences International
- Том: 55
- Номер: 3
- Год издания: 2016
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 341
- Последняя страница: 364
- DOI: 10.1134/S1064230716030163
- Аннотация: 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 selfsimilarity 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. DOI: 10.1134/S1064230716030163
- Добавил в систему: Голубев Юрий Филиппович