Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system
Apstrakt
The problem of the brachistochronic motion of a holonomic scleronomic mechanical system is analyzed. The system moves in an arbitrary field of known potential forces. The problem is formulated as an optimal control task, where generalized speeds are taken as control variables. The problem considered is reduced to solving the corresponding two-point boundary-value problem (TPBVP). In order to determine the global minimal solution of the TPBVP, an appropriate numerical procedure based on the shooting method is presented. The global minimal solution represents the solution with the minimum time of motion. The procedure is illustrated by an example of determining the brachistochronic motion of a disk that performs plane motion in a vertical plane in a homogeneous field of gravity.
Ključne reči:
Shooting method / Optimal control / Mechanical system / Holonomic / Brachistochronic motionIzvor:
Meccanica, 2017, 52, 4-5, 795-805Izdavač:
- Springer, Dordrecht
Finansiranje / projekti:
- Dinamika hibridnih sistema složenih struktura. Mehanika materijala (RS-MESTD-Basic Research (BR or ON)-174001)
- Održivost i unapređenje mašinskih sistema u energetici i transportu primenom forenzičkog inženjerstva, eko i robust dizajna (RS-MESTD-Technological Development (TD or TR)-35006)
Napomena:
- This is the peer reviewed version of the article: Radulović, R.; Obradović, A.; Šalinić, S. Contribution to the Determination of the Global Minimum Time for the Brachistochronic Motion of a Holonomic Mechanical System. Meccanica 2017, 52 (4–5), 795–805. https://doi.org/10.1007/s11012-016-0425-z
Povezane informacije:
- Druga verzija
https://doi.org/10.1007/s11012-016-0425-z - Druga verzija
https://machinery.mas.bg.ac.rs/handle/123456789/2543
DOI: 10.1007/s11012-016-0425-z
ISSN: 0025-6455
WoS: 000394320000003
Scopus: 2-s2.0-84961674020
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Radulović, Radoslav AU - Obradović, Aleksandar AU - Šalinić, Slaviša PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4328 AB - The problem of the brachistochronic motion of a holonomic scleronomic mechanical system is analyzed. The system moves in an arbitrary field of known potential forces. The problem is formulated as an optimal control task, where generalized speeds are taken as control variables. The problem considered is reduced to solving the corresponding two-point boundary-value problem (TPBVP). In order to determine the global minimal solution of the TPBVP, an appropriate numerical procedure based on the shooting method is presented. The global minimal solution represents the solution with the minimum time of motion. The procedure is illustrated by an example of determining the brachistochronic motion of a disk that performs plane motion in a vertical plane in a homogeneous field of gravity. PB - Springer, Dordrecht T2 - Meccanica T1 - Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system EP - 805 IS - 4-5 SP - 795 VL - 52 DO - 10.1007/s11012-016-0425-z ER -
@article{ author = "Radulović, Radoslav and Obradović, Aleksandar and Šalinić, Slaviša", year = "2017", abstract = "The problem of the brachistochronic motion of a holonomic scleronomic mechanical system is analyzed. The system moves in an arbitrary field of known potential forces. The problem is formulated as an optimal control task, where generalized speeds are taken as control variables. The problem considered is reduced to solving the corresponding two-point boundary-value problem (TPBVP). In order to determine the global minimal solution of the TPBVP, an appropriate numerical procedure based on the shooting method is presented. The global minimal solution represents the solution with the minimum time of motion. The procedure is illustrated by an example of determining the brachistochronic motion of a disk that performs plane motion in a vertical plane in a homogeneous field of gravity.", publisher = "Springer, Dordrecht", journal = "Meccanica", title = "Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system", pages = "805-795", number = "4-5", volume = "52", doi = "10.1007/s11012-016-0425-z" }
Radulović, R., Obradović, A.,& Šalinić, S.. (2017). Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system. in Meccanica Springer, Dordrecht., 52(4-5), 795-805. https://doi.org/10.1007/s11012-016-0425-z
Radulović R, Obradović A, Šalinić S. Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system. in Meccanica. 2017;52(4-5):795-805. doi:10.1007/s11012-016-0425-z .
Radulović, Radoslav, Obradović, Aleksandar, Šalinić, Slaviša, "Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system" in Meccanica, 52, no. 4-5 (2017):795-805, https://doi.org/10.1007/s11012-016-0425-z . .