A new approach for the determination of the global minimum time for the Chaplygin sleigh brachistochrone problem
Abstract
A new approach for the determination of the global minimum time for the case of the brachistochronic motion of the Chaplygin sleigh is presented. The new approach is based on the use of the shooting method in solving the corresponding two-point boundary-value problem and defining either the crossing points of surfaces or the crossing points space of curves in a three-dimensional space of two costate variables and the time of the brachistochronic motion of the sleigh. A number of examples for multiple extremals of the Chaplygin sleigh brachistochrone problem are provided. In these examples, the global minimum is the solution to which the minimum time of motion corresponds.
Keywords:
Pontryagin's maximum principle / optimal control / Global minimum time / Chaplygin sleigh / brachistochroneSource:
Mathematics and Mechanics of Solids, 2017, 22, 6, 1462-1482Publisher:
- Sage Publications Ltd, London
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/123456789/4324
Related info:
DOI: 10.1177/1081286516637234
ISSN: 1081-2865
WoS: 000402887700014
Scopus: 2-s2.0-85020436709
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Radulović, Radoslav AU - Šalinić, Slaviša AU - Obradović, Aleksandar AU - Rusov, Srđan PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2528 AB - A new approach for the determination of the global minimum time for the case of the brachistochronic motion of the Chaplygin sleigh is presented. The new approach is based on the use of the shooting method in solving the corresponding two-point boundary-value problem and defining either the crossing points of surfaces or the crossing points space of curves in a three-dimensional space of two costate variables and the time of the brachistochronic motion of the sleigh. A number of examples for multiple extremals of the Chaplygin sleigh brachistochrone problem are provided. In these examples, the global minimum is the solution to which the minimum time of motion corresponds. PB - Sage Publications Ltd, London T2 - Mathematics and Mechanics of Solids T1 - A new approach for the determination of the global minimum time for the Chaplygin sleigh brachistochrone problem EP - 1482 IS - 6 SP - 1462 VL - 22 DO - 10.1177/1081286516637234 ER -
@article{ author = "Radulović, Radoslav and Šalinić, Slaviša and Obradović, Aleksandar and Rusov, Srđan", year = "2017", abstract = "A new approach for the determination of the global minimum time for the case of the brachistochronic motion of the Chaplygin sleigh is presented. The new approach is based on the use of the shooting method in solving the corresponding two-point boundary-value problem and defining either the crossing points of surfaces or the crossing points space of curves in a three-dimensional space of two costate variables and the time of the brachistochronic motion of the sleigh. A number of examples for multiple extremals of the Chaplygin sleigh brachistochrone problem are provided. In these examples, the global minimum is the solution to which the minimum time of motion corresponds.", publisher = "Sage Publications Ltd, London", journal = "Mathematics and Mechanics of Solids", title = "A new approach for the determination of the global minimum time for the Chaplygin sleigh brachistochrone problem", pages = "1482-1462", number = "6", volume = "22", doi = "10.1177/1081286516637234" }
Radulović, R., Šalinić, S., Obradović, A.,& Rusov, S.. (2017). A new approach for the determination of the global minimum time for the Chaplygin sleigh brachistochrone problem. in Mathematics and Mechanics of Solids Sage Publications Ltd, London., 22(6), 1462-1482. https://doi.org/10.1177/1081286516637234
Radulović R, Šalinić S, Obradović A, Rusov S. A new approach for the determination of the global minimum time for the Chaplygin sleigh brachistochrone problem. in Mathematics and Mechanics of Solids. 2017;22(6):1462-1482. doi:10.1177/1081286516637234 .
Radulović, Radoslav, Šalinić, Slaviša, Obradović, Aleksandar, Rusov, Srđan, "A new approach for the determination of the global minimum time for the Chaplygin sleigh brachistochrone problem" in Mathematics and Mechanics of Solids, 22, no. 6 (2017):1462-1482, https://doi.org/10.1177/1081286516637234 . .