Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields
Abstract
In this paper, the brachistochronic motion of a mechanical system composed of variable-mass particles is analysed. Workless (ideal) holonomic and linear nonholonomic constraints are imposed on the system. It is assumed that the system moves in an arbitrary field of known potential and nonpotential forces with prescribed both laws of the time-rate of mass variation of the particles and relative velocities of the expelled (or gained) masses. The first time-derivatives of quasi-velocities are taken as control variables. Using Pontryagin's maximum principle and singular optimal control theory, the problem of brachistochronic motion of the nonholonomic variable-mass mechanical system is solved as a two-point boundary value problem. In addition, a discussion about the realization of control forces is given. The results are illustrated via an example.
Keywords:
variable mass / singular controls / nonholonomic constraints / Chaplygin sleigh / BrachistochroneSource:
Mathematics and Mechanics of Solids, 2019, 24, 1, 281-298Publisher:
- 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)
DOI: 10.1177/1081286517738307
ISSN: 1081-2865
WoS: 000454517400015
Scopus: 2-s2.0-85044785724
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Jeremić, Bojan AU - Radulović, Radoslav AU - Obradović, Aleksandar AU - Šalinić, Slaviša AU - Dražić, Milan PY - 2019 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3045 AB - In this paper, the brachistochronic motion of a mechanical system composed of variable-mass particles is analysed. Workless (ideal) holonomic and linear nonholonomic constraints are imposed on the system. It is assumed that the system moves in an arbitrary field of known potential and nonpotential forces with prescribed both laws of the time-rate of mass variation of the particles and relative velocities of the expelled (or gained) masses. The first time-derivatives of quasi-velocities are taken as control variables. Using Pontryagin's maximum principle and singular optimal control theory, the problem of brachistochronic motion of the nonholonomic variable-mass mechanical system is solved as a two-point boundary value problem. In addition, a discussion about the realization of control forces is given. The results are illustrated via an example. PB - Sage Publications Ltd, London T2 - Mathematics and Mechanics of Solids T1 - Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields EP - 298 IS - 1 SP - 281 VL - 24 DO - 10.1177/1081286517738307 ER -
@article{ author = "Jeremić, Bojan and Radulović, Radoslav and Obradović, Aleksandar and Šalinić, Slaviša and Dražić, Milan", year = "2019", abstract = "In this paper, the brachistochronic motion of a mechanical system composed of variable-mass particles is analysed. Workless (ideal) holonomic and linear nonholonomic constraints are imposed on the system. It is assumed that the system moves in an arbitrary field of known potential and nonpotential forces with prescribed both laws of the time-rate of mass variation of the particles and relative velocities of the expelled (or gained) masses. The first time-derivatives of quasi-velocities are taken as control variables. Using Pontryagin's maximum principle and singular optimal control theory, the problem of brachistochronic motion of the nonholonomic variable-mass mechanical system is solved as a two-point boundary value problem. In addition, a discussion about the realization of control forces is given. The results are illustrated via an example.", publisher = "Sage Publications Ltd, London", journal = "Mathematics and Mechanics of Solids", title = "Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields", pages = "298-281", number = "1", volume = "24", doi = "10.1177/1081286517738307" }
Jeremić, B., Radulović, R., Obradović, A., Šalinić, S.,& Dražić, M.. (2019). Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields. in Mathematics and Mechanics of Solids Sage Publications Ltd, London., 24(1), 281-298. https://doi.org/10.1177/1081286517738307
Jeremić B, Radulović R, Obradović A, Šalinić S, Dražić M. Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields. in Mathematics and Mechanics of Solids. 2019;24(1):281-298. doi:10.1177/1081286517738307 .
Jeremić, Bojan, Radulović, Radoslav, Obradović, Aleksandar, Šalinić, Slaviša, Dražić, Milan, "Brachistochronic motion of a nonholonomic variable-mass mechanical system in general force fields" in Mathematics and Mechanics of Solids, 24, no. 1 (2019):281-298, https://doi.org/10.1177/1081286517738307 . .