Contribution to the determination of the global minimum time for the brachistochronic motion of a holonomic mechanical system
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.
Keywords:
Shooting method / Optimal control / Mechanical system / Holonomic / Brachistochronic motionSource:
Meccanica, 2017, 52, 4-5, 795-805Publisher:
- Springer, Dordrecht
Funding / projects:
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
- Sustainability and improvement of mechanical systems in energetic, material handling and conveying by using forensic engineering, environmental and robust design (RS-MESTD-Technological Development (TD or TR)-35006)
Note:
- Peer reviewed version of the article: https://machinery.mas.bg.ac.rs/handle/123456789/4328
Related info:
DOI: 10.1007/s11012-016-0425-z
ISSN: 0025-6455
WoS: 000394320000003
Scopus: 2-s2.0-84961674020
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Radulović, Radoslav AU - Obradović, Aleksandar AU - Šalinić, Slaviša PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2543 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 . .