On the brachistochronic motion of mechanical systems with unilateral constraints
Abstract
The problem of brachistochronic motion of a two-degree of freedom mechanical system is considered. The ideal bilateral constraints and one unilateral constraint with Coulomb friction are imposed on the system. It has been assumed that the components of the metric tensor are constant. After introducing the transformation of generalized coordinates, whereby the quadratic form of kinetic energy is reduced to a canonical form, the considered problem is geometrically interpreted as the motion of a representative point in a two-dimensional Euclidean space. Thus, the analogy with the brachistochronic motion of a particle along a curve which is treated as a unilateral constraint is achieved. The results are illustrated via an example.
Keywords:
Unilateral constraints / Optimal control / Mechanical system / Coulomb friction / BrachistochroneSource:
Mechanics Research Communications, 2012, 45, 1-6Publisher:
- Pergamon-Elsevier Science Ltd, Oxford
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: 10.1016/j.mechrescom.2012.06.006
ISSN: 0093-6413
WoS: 000309803000001
Scopus: 2-s2.0-84864042070
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Šalinić, Slaviša AU - Obradović, Aleksandar AU - Mitrović, Zoran PY - 2012 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1490 AB - The problem of brachistochronic motion of a two-degree of freedom mechanical system is considered. The ideal bilateral constraints and one unilateral constraint with Coulomb friction are imposed on the system. It has been assumed that the components of the metric tensor are constant. After introducing the transformation of generalized coordinates, whereby the quadratic form of kinetic energy is reduced to a canonical form, the considered problem is geometrically interpreted as the motion of a representative point in a two-dimensional Euclidean space. Thus, the analogy with the brachistochronic motion of a particle along a curve which is treated as a unilateral constraint is achieved. The results are illustrated via an example. PB - Pergamon-Elsevier Science Ltd, Oxford T2 - Mechanics Research Communications T1 - On the brachistochronic motion of mechanical systems with unilateral constraints EP - 6 SP - 1 VL - 45 DO - 10.1016/j.mechrescom.2012.06.006 ER -
@article{ author = "Šalinić, Slaviša and Obradović, Aleksandar and Mitrović, Zoran", year = "2012", abstract = "The problem of brachistochronic motion of a two-degree of freedom mechanical system is considered. The ideal bilateral constraints and one unilateral constraint with Coulomb friction are imposed on the system. It has been assumed that the components of the metric tensor are constant. After introducing the transformation of generalized coordinates, whereby the quadratic form of kinetic energy is reduced to a canonical form, the considered problem is geometrically interpreted as the motion of a representative point in a two-dimensional Euclidean space. Thus, the analogy with the brachistochronic motion of a particle along a curve which is treated as a unilateral constraint is achieved. The results are illustrated via an example.", publisher = "Pergamon-Elsevier Science Ltd, Oxford", journal = "Mechanics Research Communications", title = "On the brachistochronic motion of mechanical systems with unilateral constraints", pages = "6-1", volume = "45", doi = "10.1016/j.mechrescom.2012.06.006" }
Šalinić, S., Obradović, A.,& Mitrović, Z.. (2012). On the brachistochronic motion of mechanical systems with unilateral constraints. in Mechanics Research Communications Pergamon-Elsevier Science Ltd, Oxford., 45, 1-6. https://doi.org/10.1016/j.mechrescom.2012.06.006
Šalinić S, Obradović A, Mitrović Z. On the brachistochronic motion of mechanical systems with unilateral constraints. in Mechanics Research Communications. 2012;45:1-6. doi:10.1016/j.mechrescom.2012.06.006 .
Šalinić, Slaviša, Obradović, Aleksandar, Mitrović, Zoran, "On the brachistochronic motion of mechanical systems with unilateral constraints" in Mechanics Research Communications, 45 (2012):1-6, https://doi.org/10.1016/j.mechrescom.2012.06.006 . .