On the brachistochrone of a variable mass particle in general force fields
Апстракт
The problem of the brachistochronic motion of a variable mass particle is considered. The particle moves through a resistant medium in the field of arbitrary active forces. Beginning from these general assumptions, and applying Pontryagin's minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained and solved. The solution proposed involves an appropriate numerical procedure based upon the shooting method. In this numerical procedure, the evaluation of ranges for unknown values of costate variables is avoided by the choice of a corresponding Cartesian coordinate of the particle as an independent variable. A numerical example assuming the resistance force proportional to the square of the particle speed is presented. A review of existing results for related problems is provided, and it can be shown that these problems may be regarded as special cases of the brachistochrone problem formulated and solved in this paper under v...ery general assumptions by means of optimal control theory.
Кључне речи:
Variable mass particle / Singular optimal control / Pontryagin's minimum principle / BrachistochroneИзвор:
Mathematical and Computer Modelling, 2011, 54, 11-12, 2900-2912Издавач:
- Pergamon-Elsevier Science Ltd, Oxford
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: 10.1016/j.mcm.2011.07.011
ISSN: 0895-7177
WoS: 000295716700034
Scopus: 2-s2.0-80052612166
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Jeremić, Olivera AU - Šalinić, Slaviša AU - Obradović, Aleksandar AU - Mitrović, Zoran PY - 2011 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1202 AB - The problem of the brachistochronic motion of a variable mass particle is considered. The particle moves through a resistant medium in the field of arbitrary active forces. Beginning from these general assumptions, and applying Pontryagin's minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained and solved. The solution proposed involves an appropriate numerical procedure based upon the shooting method. In this numerical procedure, the evaluation of ranges for unknown values of costate variables is avoided by the choice of a corresponding Cartesian coordinate of the particle as an independent variable. A numerical example assuming the resistance force proportional to the square of the particle speed is presented. A review of existing results for related problems is provided, and it can be shown that these problems may be regarded as special cases of the brachistochrone problem formulated and solved in this paper under very general assumptions by means of optimal control theory. PB - Pergamon-Elsevier Science Ltd, Oxford T2 - Mathematical and Computer Modelling T1 - On the brachistochrone of a variable mass particle in general force fields EP - 2912 IS - 11-12 SP - 2900 VL - 54 DO - 10.1016/j.mcm.2011.07.011 ER -
@article{ author = "Jeremić, Olivera and Šalinić, Slaviša and Obradović, Aleksandar and Mitrović, Zoran", year = "2011", abstract = "The problem of the brachistochronic motion of a variable mass particle is considered. The particle moves through a resistant medium in the field of arbitrary active forces. Beginning from these general assumptions, and applying Pontryagin's minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained and solved. The solution proposed involves an appropriate numerical procedure based upon the shooting method. In this numerical procedure, the evaluation of ranges for unknown values of costate variables is avoided by the choice of a corresponding Cartesian coordinate of the particle as an independent variable. A numerical example assuming the resistance force proportional to the square of the particle speed is presented. A review of existing results for related problems is provided, and it can be shown that these problems may be regarded as special cases of the brachistochrone problem formulated and solved in this paper under very general assumptions by means of optimal control theory.", publisher = "Pergamon-Elsevier Science Ltd, Oxford", journal = "Mathematical and Computer Modelling", title = "On the brachistochrone of a variable mass particle in general force fields", pages = "2912-2900", number = "11-12", volume = "54", doi = "10.1016/j.mcm.2011.07.011" }
Jeremić, O., Šalinić, S., Obradović, A.,& Mitrović, Z.. (2011). On the brachistochrone of a variable mass particle in general force fields. in Mathematical and Computer Modelling Pergamon-Elsevier Science Ltd, Oxford., 54(11-12), 2900-2912. https://doi.org/10.1016/j.mcm.2011.07.011
Jeremić O, Šalinić S, Obradović A, Mitrović Z. On the brachistochrone of a variable mass particle in general force fields. in Mathematical and Computer Modelling. 2011;54(11-12):2900-2912. doi:10.1016/j.mcm.2011.07.011 .
Jeremić, Olivera, Šalinić, Slaviša, Obradović, Aleksandar, Mitrović, Zoran, "On the brachistochrone of a variable mass particle in general force fields" in Mathematical and Computer Modelling, 54, no. 11-12 (2011):2900-2912, https://doi.org/10.1016/j.mcm.2011.07.011 . .