On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution
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2022
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The paper considers a heavy homogeneous ball rolling without slipping on the outside of a real rough fixed surface of revolution, which is generated by rotating a plane curve around a vertical axis. By applying the Coulomb sliding friction law, the position is established at which slipping occurs during rolling down the surface, and thereafter this mechanical system ceases to be holonomic. Dynamic differential equations of motion are obtained using general theorems of mechanics. The paper presents the procedure of determining the tangential and normal component of the reaction of constraint depending on the height of the contact point between the ball and the surface. On the basis of the initial total mechanical energy of the system and the value of Coulomb friction coefficient, the condition is determined to prevent the ball from slipping, as well as the height interval in which the considered system behaves as a nonholonomic system. The procedure is illustrated by examples of surface...s generated by rotating segments of the circular arc, line and parabola. In the last example there is not a closed-form solution, so that numerical integration of a corresponding Cauchy problem is performed.
Ključne reči:
rolling without slipping / point contact / nonholonomic mechanics / heavy ball / dynamics / Coulomb frictionIzvor:
Applied Mathematics and Computation, 2022, 420Izdavač:
- Elsevier Science Inc, New York
Finansiranje / projekti:
- Ministarstvo nauke, tehnološkog razvoja i inovacija Republike Srbije, institucionalno finansiranje - 200105 (Univerzitet u Beogradu, Mašinski fakultet) (RS-MESTD-inst-2020-200105)
- Ministarstvo nauke, tehnološkog razvoja i inovacija Republike Srbije, institucionalno finansiranje - 200108 (Univerzitet u Kragujevcu, Mašinski fakultet, Kraljevo) (RS-MESTD-inst-2020-200108)
Napomena:
- Peer reviewed version of the article: https://machinery.mas.bg.ac.rs/handle/123456789/4361
Povezane informacije:
- Druga verzija
https://machinery.mas.bg.ac.rs/handle/123456789/4361
DOI: 10.1016/j.amc.2021.126906
ISSN: 0096-3003
WoS: 000798062800017
Scopus: 2-s2.0-85122516340
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Obradović, Aleksandar AU - Mitrović, Zoran AU - Šalinić, Slaviša PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3691 AB - The paper considers a heavy homogeneous ball rolling without slipping on the outside of a real rough fixed surface of revolution, which is generated by rotating a plane curve around a vertical axis. By applying the Coulomb sliding friction law, the position is established at which slipping occurs during rolling down the surface, and thereafter this mechanical system ceases to be holonomic. Dynamic differential equations of motion are obtained using general theorems of mechanics. The paper presents the procedure of determining the tangential and normal component of the reaction of constraint depending on the height of the contact point between the ball and the surface. On the basis of the initial total mechanical energy of the system and the value of Coulomb friction coefficient, the condition is determined to prevent the ball from slipping, as well as the height interval in which the considered system behaves as a nonholonomic system. The procedure is illustrated by examples of surfaces generated by rotating segments of the circular arc, line and parabola. In the last example there is not a closed-form solution, so that numerical integration of a corresponding Cauchy problem is performed. PB - Elsevier Science Inc, New York T2 - Applied Mathematics and Computation T1 - On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution VL - 420 DO - 10.1016/j.amc.2021.126906 ER -
@article{ author = "Obradović, Aleksandar and Mitrović, Zoran and Šalinić, Slaviša", year = "2022", abstract = "The paper considers a heavy homogeneous ball rolling without slipping on the outside of a real rough fixed surface of revolution, which is generated by rotating a plane curve around a vertical axis. By applying the Coulomb sliding friction law, the position is established at which slipping occurs during rolling down the surface, and thereafter this mechanical system ceases to be holonomic. Dynamic differential equations of motion are obtained using general theorems of mechanics. The paper presents the procedure of determining the tangential and normal component of the reaction of constraint depending on the height of the contact point between the ball and the surface. On the basis of the initial total mechanical energy of the system and the value of Coulomb friction coefficient, the condition is determined to prevent the ball from slipping, as well as the height interval in which the considered system behaves as a nonholonomic system. The procedure is illustrated by examples of surfaces generated by rotating segments of the circular arc, line and parabola. In the last example there is not a closed-form solution, so that numerical integration of a corresponding Cauchy problem is performed.", publisher = "Elsevier Science Inc, New York", journal = "Applied Mathematics and Computation", title = "On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution", volume = "420", doi = "10.1016/j.amc.2021.126906" }
Obradović, A., Mitrović, Z.,& Šalinić, S.. (2022). On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution. in Applied Mathematics and Computation Elsevier Science Inc, New York., 420. https://doi.org/10.1016/j.amc.2021.126906
Obradović A, Mitrović Z, Šalinić S. On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution. in Applied Mathematics and Computation. 2022;420. doi:10.1016/j.amc.2021.126906 .
Obradović, Aleksandar, Mitrović, Zoran, Šalinić, Slaviša, "On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution" in Applied Mathematics and Computation, 420 (2022), https://doi.org/10.1016/j.amc.2021.126906 . .