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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system
Bojan Jeremić, Radoslav Radulović, Aleksandar Obradović Department of Mechanics,
Faculty of Mechanical Engineering,
University of Belgrade,
Belgrade,
Serbia
Аннотация:
The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] in a horizontal plane, between two specified positions.
Variable mass particles are interconnected by a lightweight mechanism of the ‘pitchfork’ type.
The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, are known. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are created based on the general theorems of dynamics of a variable mass mechanical system [5].
The formulated brachistochrone problem, with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal control by applying Pontryagin's maximum principle [1].
A corresponding two-point boundary value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained, which, in a general case, has to be numerically solved [2].
On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are determined.
The analysis of the brachistochronic motion for different values of the initial position of a variable mass particle $B$ is presented.
Also, the interval of values of the initial position of a variable mass particle $B$, for which there are the TPBVP solutions, is determined.
Ключевые слова:
brachistochrone, variable mass, nonholonomic system, Pontryagin's maximum principle, optimal control.
Поступила в редакцию: 23.07.2015 Исправленный вариант: 04.04.2016
Образец цитирования:
Bojan Jeremić, Radoslav Radulović, Aleksandar Obradović, “Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system”, Theor. Appl. Mech., 43:1 (2016), 19–32
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tam4 https://www.mathnet.ru/rus/tam/v43/i1/p19
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Страница аннотации: | 95 | PDF полного текста: | 23 | Список литературы: | 16 |
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