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Theoretical and Applied Mechanics, 2023, Volume 50, Issue 2, Pages 171–183
DOI: https://doi.org/https://doi.org/10.2298/TAM231017011O
(Mi tam134)
 

Realization of the brachistochronic motion of Chaplygin sleigh in a vertical plane with an unilateral nonholonomic constraint

Aleksandar M. Obradovića, Oleg Yu. Cherkasovbc, Luka N. Miličića, Slaviša Šalinićd

a Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
c Faculty of Computational Mathematics and Cybernatics, Shenzhen MSU-BIT University, Shenzhen, P.R. China
d Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Kraljevo, Serbia
References:
Abstract: The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade is such that it prevents the motion of the contact point in one direction only. The position of the sleigh mass center and orientation at the final positions is specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by applying Pontryagin’s maximum principle. For some cases, analytical solutions of differential equations of the two-point boundary value problem (TPBVP) of the maximum principle were found. Numerical integration was carried out for other cases using the shooting method, where the assessment of missing terminal conditions was given and it was shown that the solution obtained represents the global minimum time for the brachistochronic motion. The method of the brachistochronic motion by means of a single holonomic and a single unilateral nonholonomic mechanical constraint is presented.
Keywords: Chaplygin sleigh, maximum principle, unilateral nonholonomic constraint, analytical solutions.
Funding agency Grant number
Ministry of Education, Science and Technical Development of Serbia 451-03-47/2023-01/200105
451-03-47/2023-01/200108
This research was supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (Grants No. 451-03-47/2023-01/200105 and No. 451-03-47/2023-01/200108).
Received: 17.10.2023
Accepted: 29.11.2023
Document Type: Article
MSC: 70E18, 70Q05, 49N90
Language: English
Citation: Aleksandar M. Obradović, Oleg Yu. Cherkasov, Luka N. Miličić, Slaviša Šalinić, “Realization of the brachistochronic motion of Chaplygin sleigh in a vertical plane with an unilateral nonholonomic constraint”, Theor. Appl. Mech., 50:2 (2023), 171–183
Citation in format AMSBIB
\Bibitem{ObrCheMil23}
\by Aleksandar~M.~Obradovi\'c, Oleg~Yu.~Cherkasov, Luka~N.~Mili{\v{c}}i{\'c}, Slavi{\v s}a~{\v S}alini\'c
\paper Realization of the brachistochronic motion of Chaplygin sleigh in a vertical plane with an unilateral nonholonomic constraint
\jour Theor. Appl. Mech.
\yr 2023
\vol 50
\issue 2
\pages 171--183
\mathnet{http://mi.mathnet.ru/tam134}
\crossref{https://doi.org/https://doi.org/10.2298/TAM231017011O}
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  • https://www.mathnet.ru/eng/tam/v50/i2/p171
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