Brachistochronic motion of a nonholonomic rheonomic mechanical system
Само за регистроване кориснике
2010
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
The brachistochrone problem of the rheonomic mechanical system whose motion is subject to nonholonomic constraints is solved with nonlinear differential equations of motion. Apart from control forces, the system is influenced by the action of other known potential and nonpotential forces as well. The problem of optimal control is solved by applying Pontryagin's Maximum Principle and the singular optimal control theory. This procedure results in the two-point boundary value problem for the system of ordinary nonlinear differential equations of the first order, with a corresponding number of initial and end conditions. This paper determines the control forces that are realized by imposing on the system a corresponding number of independent ideal holonomic constraints, without the action of active control forces. These constraints must be in accordance with the previously determined brachistochronic motion. The method is illustrated with a single complex example that represents the first ...known concrete demonstration of brachistochronic motion of the nonholonomic rheonomic mechanical system.
Извор:
Acta Mechanica, 2010, 214, 3-4, 291-304Издавач:
- Springer Wien, Wien
Финансирање / пројекти:
- Савремени проблеми механике деформабилног тела (RS-MESTD-MPN2006-2010-144019)
- Развој машина високих перформанси и метода за идентификацију њиховог одзива на унутрашње и спољашње поремећаје (RS-MESTD-MPN2006-2010-14052)
DOI: 10.1007/s00707-010-0295-8
ISSN: 0001-5970
WoS: 000283084200005
Scopus: 2-s2.0-78149284670
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Obradović, Aleksandar AU - Cović, V. AU - Vesković, M. AU - Dražić, Milan PY - 2010 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1110 AB - The brachistochrone problem of the rheonomic mechanical system whose motion is subject to nonholonomic constraints is solved with nonlinear differential equations of motion. Apart from control forces, the system is influenced by the action of other known potential and nonpotential forces as well. The problem of optimal control is solved by applying Pontryagin's Maximum Principle and the singular optimal control theory. This procedure results in the two-point boundary value problem for the system of ordinary nonlinear differential equations of the first order, with a corresponding number of initial and end conditions. This paper determines the control forces that are realized by imposing on the system a corresponding number of independent ideal holonomic constraints, without the action of active control forces. These constraints must be in accordance with the previously determined brachistochronic motion. The method is illustrated with a single complex example that represents the first known concrete demonstration of brachistochronic motion of the nonholonomic rheonomic mechanical system. PB - Springer Wien, Wien T2 - Acta Mechanica T1 - Brachistochronic motion of a nonholonomic rheonomic mechanical system EP - 304 IS - 3-4 SP - 291 VL - 214 DO - 10.1007/s00707-010-0295-8 ER -
@article{ author = "Obradović, Aleksandar and Cović, V. and Vesković, M. and Dražić, Milan", year = "2010", abstract = "The brachistochrone problem of the rheonomic mechanical system whose motion is subject to nonholonomic constraints is solved with nonlinear differential equations of motion. Apart from control forces, the system is influenced by the action of other known potential and nonpotential forces as well. The problem of optimal control is solved by applying Pontryagin's Maximum Principle and the singular optimal control theory. This procedure results in the two-point boundary value problem for the system of ordinary nonlinear differential equations of the first order, with a corresponding number of initial and end conditions. This paper determines the control forces that are realized by imposing on the system a corresponding number of independent ideal holonomic constraints, without the action of active control forces. These constraints must be in accordance with the previously determined brachistochronic motion. The method is illustrated with a single complex example that represents the first known concrete demonstration of brachistochronic motion of the nonholonomic rheonomic mechanical system.", publisher = "Springer Wien, Wien", journal = "Acta Mechanica", title = "Brachistochronic motion of a nonholonomic rheonomic mechanical system", pages = "304-291", number = "3-4", volume = "214", doi = "10.1007/s00707-010-0295-8" }
Obradović, A., Cović, V., Vesković, M.,& Dražić, M.. (2010). Brachistochronic motion of a nonholonomic rheonomic mechanical system. in Acta Mechanica Springer Wien, Wien., 214(3-4), 291-304. https://doi.org/10.1007/s00707-010-0295-8
Obradović A, Cović V, Vesković M, Dražić M. Brachistochronic motion of a nonholonomic rheonomic mechanical system. in Acta Mechanica. 2010;214(3-4):291-304. doi:10.1007/s00707-010-0295-8 .
Obradović, Aleksandar, Cović, V., Vesković, M., Dražić, Milan, "Brachistochronic motion of a nonholonomic rheonomic mechanical system" in Acta Mechanica, 214, no. 3-4 (2010):291-304, https://doi.org/10.1007/s00707-010-0295-8 . .