TY  - CONF
AU  - Obradović, Aleksandar
AU  - Cherkasov, Oleg
AU  - Miličić, Luka
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6897
AB  - 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.
PB  - Belgrade : Serbian Society of Mechanics
C3  - 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023
T1  - THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT
SP  - T.4.3
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6897
ER  - 

@conference{
author = "Obradović, Aleksandar and Cherkasov, Oleg and Miličić, Luka",
year = "2023",
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.",
publisher = "Belgrade : Serbian Society of Mechanics",
journal = "9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023",
title = "THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT",
pages = "T.4.3",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6897"
}

Obradović, A., Cherkasov, O.,& Miličić, L.. (2023). THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023
Belgrade : Serbian Society of Mechanics., T.4.3.
https://hdl.handle.net/21.15107/rcub_machinery_6897

Obradović A, Cherkasov O, Miličić L. THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023. 2023;:T.4.3.
https://hdl.handle.net/21.15107/rcub_machinery_6897 .

Obradović, Aleksandar, Cherkasov, Oleg, Miličić, Luka, "THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT" in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023 (2023):T.4.3,
https://hdl.handle.net/21.15107/rcub_machinery_6897 .

TY  - JOUR
AU  - Obradović, Aleksandar
AU  - Cherkasov, Oleg
AU  - Miličić, Luka
AU  - Šalinić, Slaviša
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7711
AB  - 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.
PB  - Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd
T1  - REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT
EP  - 183
IS  - 2
SP  - 171
VL  - 50
DO  - 10.2298/TAM231017011O
ER  - 

@article{
author = "Obradović, Aleksandar and Cherkasov, Oleg and Miličić, Luka and Šalinić, Slaviša",
year = "2023",
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.",
publisher = "Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd",
title = "REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT",
pages = "183-171",
number = "2",
volume = "50",
doi = "10.2298/TAM231017011O"
}

Obradović, A., Cherkasov, O., Miličić, L.,& Šalinić, S.. (2023). REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. 
Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd., 50(2), 171-183.
https://doi.org/10.2298/TAM231017011O

Obradović A, Cherkasov O, Miličić L, Šalinić S. REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. 2023;50(2):171-183.
doi:10.2298/TAM231017011O .

Obradović, Aleksandar, Cherkasov, Oleg, Miličić, Luka, Šalinić, Slaviša, "REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT", 50, no. 2 (2023):171-183,
https://doi.org/10.2298/TAM231017011O . .