REALIZATION OF THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT
2023
Чланак у часопису (Објављена верзија)
,
Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd
Метаподаци
Приказ свих података о документуАпстракт
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.
Извор:
2023, 50, 2, 171-183Издавач:
- Serbian Society of Mechanics and Mathematical Institute of the Serbian Academy of Sciences and Arts, Beograd
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200108 (Универзитет у Крагујевцу, Машински факултет, Краљево) (RS-MESTD-inst-2020-200108)
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
Колекције
Институција/група
Mašinski fakultetTY - 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 . .