A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value
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2018
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We consider the brachistochrone problem of the particle with a preselected interval for the normal reaction force value as well as the terminal position of the particle lying on an arbitrary planar curve. We use optimal control theory to solve the formulated brachistochrone problem. Here we treat the brachistochrone curve as a bilateral ideal constraint. We study the cases of symmetrically and unsymmetrically preselected intervals for the normal reaction force value. We show that in the case of a symmetrically preselected interval for the normal reaction force value, the brachistochrone curve is a two-segment curve, and in the case of an unsymmetrically preselected interval, it is a three-segment curve. We present a numerical procedure for the identification of the global minimum time of motion. Finally, we present several examples to illustrate the approach proposed in the paper.
Ključne reči:
Singular control / Optimal control / Global minimum time / BrachistochroneIzvor:
International Journal of Non-Linear Mechanics, 2018, 101, 26-35Izdavač:
- Pergamon-Elsevier Science Ltd, Oxford
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)
DOI: 10.1016/j.ijnonlinmec.2018.02.001
ISSN: 0020-7462
WoS: 000431747900004
Scopus: 2-s2.0-85042371132
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Radulović, Radoslav AU - Jeremić, Bojan AU - Šalinić, Slaviša AU - Obradović, Aleksandar AU - Dražić, Milan PY - 2018 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2931 AB - We consider the brachistochrone problem of the particle with a preselected interval for the normal reaction force value as well as the terminal position of the particle lying on an arbitrary planar curve. We use optimal control theory to solve the formulated brachistochrone problem. Here we treat the brachistochrone curve as a bilateral ideal constraint. We study the cases of symmetrically and unsymmetrically preselected intervals for the normal reaction force value. We show that in the case of a symmetrically preselected interval for the normal reaction force value, the brachistochrone curve is a two-segment curve, and in the case of an unsymmetrically preselected interval, it is a three-segment curve. We present a numerical procedure for the identification of the global minimum time of motion. Finally, we present several examples to illustrate the approach proposed in the paper. PB - Pergamon-Elsevier Science Ltd, Oxford T2 - International Journal of Non-Linear Mechanics T1 - A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value EP - 35 SP - 26 VL - 101 DO - 10.1016/j.ijnonlinmec.2018.02.001 ER -
@article{ author = "Radulović, Radoslav and Jeremić, Bojan and Šalinić, Slaviša and Obradović, Aleksandar and Dražić, Milan", year = "2018", abstract = "We consider the brachistochrone problem of the particle with a preselected interval for the normal reaction force value as well as the terminal position of the particle lying on an arbitrary planar curve. We use optimal control theory to solve the formulated brachistochrone problem. Here we treat the brachistochrone curve as a bilateral ideal constraint. We study the cases of symmetrically and unsymmetrically preselected intervals for the normal reaction force value. We show that in the case of a symmetrically preselected interval for the normal reaction force value, the brachistochrone curve is a two-segment curve, and in the case of an unsymmetrically preselected interval, it is a three-segment curve. We present a numerical procedure for the identification of the global minimum time of motion. Finally, we present several examples to illustrate the approach proposed in the paper.", publisher = "Pergamon-Elsevier Science Ltd, Oxford", journal = "International Journal of Non-Linear Mechanics", title = "A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value", pages = "35-26", volume = "101", doi = "10.1016/j.ijnonlinmec.2018.02.001" }
Radulović, R., Jeremić, B., Šalinić, S., Obradović, A.,& Dražić, M.. (2018). A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value. in International Journal of Non-Linear Mechanics Pergamon-Elsevier Science Ltd, Oxford., 101, 26-35. https://doi.org/10.1016/j.ijnonlinmec.2018.02.001
Radulović R, Jeremić B, Šalinić S, Obradović A, Dražić M. A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value. in International Journal of Non-Linear Mechanics. 2018;101:26-35. doi:10.1016/j.ijnonlinmec.2018.02.001 .
Radulović, Radoslav, Jeremić, Bojan, Šalinić, Slaviša, Obradović, Aleksandar, Dražić, Milan, "A new approach for the determination of the global minimum time for the brachistochrone with preselected interval for the normal reaction force value" in International Journal of Non-Linear Mechanics, 101 (2018):26-35, https://doi.org/10.1016/j.ijnonlinmec.2018.02.001 . .