On the brachistochronic motion of a variable-mass mechanical system in general force fields
Abstract
The problem of the brachistochronic motion of a mechanical system composed of rigid bodies and variable-mass particles is solved. The laws of the time-rate of mass variation of the particles as well as relative velocities of the expelled (or gained) masses are assumed to be known. The system moves in an arbitrary field of known potential and nonpotential forces. Applying Pontryagin's minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained. The appropriate numerical procedure based on the shooting method to solve the obtained two-point boundary value problem is presented. The considerations in the paper are illustrated by an example of determining the brachistochronic motion of a system composed of a rigid rod and two variable-mass particles attached to the rod.
Keywords:
variable mass / singular controls / Pontryagin's minimum principle / mechanical system / BrachistochroneSource:
Mathematics and Mechanics of Solids, 2014, 19, 4, 398-410Publisher:
- Sage Publications Ltd, London
Funding / projects:
- 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)
DOI: 10.1177/1081286512467563
ISSN: 1081-2865
WoS: 000340113600005
Scopus: 2-s2.0-84912054681
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Obradović, Aleksandar AU - Šalinić, Slaviša AU - Jeremić, Olivera AU - Mitrović, Zoran PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1888 AB - The problem of the brachistochronic motion of a mechanical system composed of rigid bodies and variable-mass particles is solved. The laws of the time-rate of mass variation of the particles as well as relative velocities of the expelled (or gained) masses are assumed to be known. The system moves in an arbitrary field of known potential and nonpotential forces. Applying Pontryagin's minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained. The appropriate numerical procedure based on the shooting method to solve the obtained two-point boundary value problem is presented. The considerations in the paper are illustrated by an example of determining the brachistochronic motion of a system composed of a rigid rod and two variable-mass particles attached to the rod. PB - Sage Publications Ltd, London T2 - Mathematics and Mechanics of Solids T1 - On the brachistochronic motion of a variable-mass mechanical system in general force fields EP - 410 IS - 4 SP - 398 VL - 19 DO - 10.1177/1081286512467563 ER -
@article{ author = "Obradović, Aleksandar and Šalinić, Slaviša and Jeremić, Olivera and Mitrović, Zoran", year = "2014", abstract = "The problem of the brachistochronic motion of a mechanical system composed of rigid bodies and variable-mass particles is solved. The laws of the time-rate of mass variation of the particles as well as relative velocities of the expelled (or gained) masses are assumed to be known. The system moves in an arbitrary field of known potential and nonpotential forces. Applying Pontryagin's minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained. The appropriate numerical procedure based on the shooting method to solve the obtained two-point boundary value problem is presented. The considerations in the paper are illustrated by an example of determining the brachistochronic motion of a system composed of a rigid rod and two variable-mass particles attached to the rod.", publisher = "Sage Publications Ltd, London", journal = "Mathematics and Mechanics of Solids", title = "On the brachistochronic motion of a variable-mass mechanical system in general force fields", pages = "410-398", number = "4", volume = "19", doi = "10.1177/1081286512467563" }
Obradović, A., Šalinić, S., Jeremić, O.,& Mitrović, Z.. (2014). On the brachistochronic motion of a variable-mass mechanical system in general force fields. in Mathematics and Mechanics of Solids Sage Publications Ltd, London., 19(4), 398-410. https://doi.org/10.1177/1081286512467563
Obradović A, Šalinić S, Jeremić O, Mitrović Z. On the brachistochronic motion of a variable-mass mechanical system in general force fields. in Mathematics and Mechanics of Solids. 2014;19(4):398-410. doi:10.1177/1081286512467563 .
Obradović, Aleksandar, Šalinić, Slaviša, Jeremić, Olivera, Mitrović, Zoran, "On the brachistochronic motion of a variable-mass mechanical system in general force fields" in Mathematics and Mechanics of Solids, 19, no. 4 (2014):398-410, https://doi.org/10.1177/1081286512467563 . .