On the brachistochronic motion of the Chaplygin sleigh
Само за регистроване кориснике
2013
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
This paper deals with the brachistochronic motion of the Chaplygin sleigh on a horizontal plane surface. Two cases are considered, such as: the case when the magnitude of the horizontal reaction force at the contact point of the knife edge with the surface is unbounded, and the case when the magnitude of this force is bounded. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The angular acceleration of the sleigh is taken for a control variable. The problem considered is reduced to solving the corresponding two-point boundary value problem. In order to solve the obtained boundary value problem, an appropriate numerical procedure based on the shooting method is presented. Also, the paper analyzes the influence of the bounded magnitude of the reaction force on the structure of the controller sequence. It is shown that in the case of unbounded magnitude of the reaction force, the control is singular, and in the case of bounded magnitude..., the control is, in a general case, a combination of singular and bang-bang controls.
Извор:
Acta Mechanica, 2013, 224, 9, 2127-2141Издавач:
- Springer Wien, Wien
Финансирање / пројекти:
- Одрживост и унапређење машинских система у енергетици и транспорту применом форензичког инжењерства, еко и робуст дизајна (RS-MESTD-Technological Development (TD or TR)-35006)
DOI: 10.1007/s00707-013-0878-2
ISSN: 0001-5970
WoS: 000323371700016
Scopus: 2-s2.0-84883161072
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Šalinić, Slaviša AU - Obradović, Aleksandar AU - Mitrović, Zoran AU - Rusov, Srđan PY - 2013 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1687 AB - This paper deals with the brachistochronic motion of the Chaplygin sleigh on a horizontal plane surface. Two cases are considered, such as: the case when the magnitude of the horizontal reaction force at the contact point of the knife edge with the surface is unbounded, and the case when the magnitude of this force is bounded. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The angular acceleration of the sleigh is taken for a control variable. The problem considered is reduced to solving the corresponding two-point boundary value problem. In order to solve the obtained boundary value problem, an appropriate numerical procedure based on the shooting method is presented. Also, the paper analyzes the influence of the bounded magnitude of the reaction force on the structure of the controller sequence. It is shown that in the case of unbounded magnitude of the reaction force, the control is singular, and in the case of bounded magnitude, the control is, in a general case, a combination of singular and bang-bang controls. PB - Springer Wien, Wien T2 - Acta Mechanica T1 - On the brachistochronic motion of the Chaplygin sleigh EP - 2141 IS - 9 SP - 2127 VL - 224 DO - 10.1007/s00707-013-0878-2 ER -
@article{ author = "Šalinić, Slaviša and Obradović, Aleksandar and Mitrović, Zoran and Rusov, Srđan", year = "2013", abstract = "This paper deals with the brachistochronic motion of the Chaplygin sleigh on a horizontal plane surface. Two cases are considered, such as: the case when the magnitude of the horizontal reaction force at the contact point of the knife edge with the surface is unbounded, and the case when the magnitude of this force is bounded. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The angular acceleration of the sleigh is taken for a control variable. The problem considered is reduced to solving the corresponding two-point boundary value problem. In order to solve the obtained boundary value problem, an appropriate numerical procedure based on the shooting method is presented. Also, the paper analyzes the influence of the bounded magnitude of the reaction force on the structure of the controller sequence. It is shown that in the case of unbounded magnitude of the reaction force, the control is singular, and in the case of bounded magnitude, the control is, in a general case, a combination of singular and bang-bang controls.", publisher = "Springer Wien, Wien", journal = "Acta Mechanica", title = "On the brachistochronic motion of the Chaplygin sleigh", pages = "2141-2127", number = "9", volume = "224", doi = "10.1007/s00707-013-0878-2" }
Šalinić, S., Obradović, A., Mitrović, Z.,& Rusov, S.. (2013). On the brachistochronic motion of the Chaplygin sleigh. in Acta Mechanica Springer Wien, Wien., 224(9), 2127-2141. https://doi.org/10.1007/s00707-013-0878-2
Šalinić S, Obradović A, Mitrović Z, Rusov S. On the brachistochronic motion of the Chaplygin sleigh. in Acta Mechanica. 2013;224(9):2127-2141. doi:10.1007/s00707-013-0878-2 .
Šalinić, Slaviša, Obradović, Aleksandar, Mitrović, Zoran, Rusov, Srđan, "On the brachistochronic motion of the Chaplygin sleigh" in Acta Mechanica, 224, no. 9 (2013):2127-2141, https://doi.org/10.1007/s00707-013-0878-2 . .