2017
DOI: 10.2298/tam171002015o
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The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip

Abstract: This paper deals with the brachistochronic motion of a thin uniform disk rolling on a horizontal plane without slip. The problem is formulated and solved within the frame of the optimal control theory. The brachistochronic motion of the disk is controlled by three torques. The possibility of the realization of the brachistochronic motion found in presence of Coulomb dry friction forces is inspected. Also, the influence of values of the coefficient of dry friction on the structure of the extremal trajectory is … Show more

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Cited by 10 publications
(6 citation statements)
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References 23 publications
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“…Although the wheel dynamics analysis benefits from using the non-spinning frame, [36], this does not allow the straightforward use of existing ready-to-use 6D dynamics equations as in the, for example, VDC mainstream form, where it is assumed that each body frame adopts all the body motions.…”
Section: D Vector Mobile Manipulator Dynamics a Wheel Dynamicsmentioning
confidence: 99%
“…Although the wheel dynamics analysis benefits from using the non-spinning frame, [36], this does not allow the straightforward use of existing ready-to-use 6D dynamics equations as in the, for example, VDC mainstream form, where it is assumed that each body frame adopts all the body motions.…”
Section: D Vector Mobile Manipulator Dynamics a Wheel Dynamicsmentioning
confidence: 99%
“…Динаміка руху вертикального диска по горизонтальній площині без ковзання досліджувалась у роботі A. Obradovic та ін. [27].…”
Section: вступunclassified
“…В [20][21][22] с помощью методов вариационного исчисления получены уравнения брахистохроны для тяжелого однородного цилиндра, катящегося без скольжения по вогнутой цилиндрической выемке, и доказана изохронность колебаний его центра масс. В [23] В работе [28] в рамках теории оптимального управления объектами сделана попытка в аналитическом и численном виде определить оптимальное по быстродействию управление для произвольного поля скоростей. Критерием качества выбрано время попадания точки в конечное состояние, а в качестве функционала взят функционал Больца [24].…”
Section: Introductionunclassified