On the instability of equilibrium position of a mechanical system with singular constraints
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2013
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The Lyapunov first method generalized to the case of nonlinear differential equations is applied to the study of the instability of the equilibrium position of a mechanical system, whose motion is constrained by singular nonholonomic constraints. Starting from the results of S. D. Furta (On the instability of equilibrium position of constrained mechanical systems) three theorems on the instability are formulated. The first theorem considers the case of nonholonomic constraints that do not satisfy the condition of weak nonholonomity. The other two theorems are related to the case of weakly nonholonomic systems. In each of the formulated theorems it is shown that the minimum form of Maclaurin series for the potential energy has not a local minimum. Thus, a contribution has been made to the inversion of Lagrange's theorem.
Ključne reči:
singular constraints / nonholonomic system / Lyapunov first method / instability of equilibriumIzvor:
Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 2013, 93, 12, 928-936Izdavač:
- Wiley-V C H Verlag Gmbh, Weinheim
Finansiranje / projekti:
- Održivost i unapređenje mašinskih sistema u energetici i transportu primenom forenzičkog inženjerstva, eko i robust dizajna (RS-MESTD-Technological Development (TD or TR)-35006)
DOI: 10.1002/zamm.201200080
ISSN: 0044-2267
WoS: 000329941900006
Scopus: 2-s2.0-84910089667
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Institucija/grupa
Mašinski fakultetTY - JOUR AU - Cović, V. AU - Mitrović, Zoran AU - Rusov, Srđan AU - Obradović, Aleksandar PY - 2013 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1704 AB - The Lyapunov first method generalized to the case of nonlinear differential equations is applied to the study of the instability of the equilibrium position of a mechanical system, whose motion is constrained by singular nonholonomic constraints. Starting from the results of S. D. Furta (On the instability of equilibrium position of constrained mechanical systems) three theorems on the instability are formulated. The first theorem considers the case of nonholonomic constraints that do not satisfy the condition of weak nonholonomity. The other two theorems are related to the case of weakly nonholonomic systems. In each of the formulated theorems it is shown that the minimum form of Maclaurin series for the potential energy has not a local minimum. Thus, a contribution has been made to the inversion of Lagrange's theorem. PB - Wiley-V C H Verlag Gmbh, Weinheim T2 - Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik T1 - On the instability of equilibrium position of a mechanical system with singular constraints EP - 936 IS - 12 SP - 928 VL - 93 DO - 10.1002/zamm.201200080 ER -
@article{ author = "Cović, V. and Mitrović, Zoran and Rusov, Srđan and Obradović, Aleksandar", year = "2013", abstract = "The Lyapunov first method generalized to the case of nonlinear differential equations is applied to the study of the instability of the equilibrium position of a mechanical system, whose motion is constrained by singular nonholonomic constraints. Starting from the results of S. D. Furta (On the instability of equilibrium position of constrained mechanical systems) three theorems on the instability are formulated. The first theorem considers the case of nonholonomic constraints that do not satisfy the condition of weak nonholonomity. The other two theorems are related to the case of weakly nonholonomic systems. In each of the formulated theorems it is shown that the minimum form of Maclaurin series for the potential energy has not a local minimum. Thus, a contribution has been made to the inversion of Lagrange's theorem.", publisher = "Wiley-V C H Verlag Gmbh, Weinheim", journal = "Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik", title = "On the instability of equilibrium position of a mechanical system with singular constraints", pages = "936-928", number = "12", volume = "93", doi = "10.1002/zamm.201200080" }
Cović, V., Mitrović, Z., Rusov, S.,& Obradović, A.. (2013). On the instability of equilibrium position of a mechanical system with singular constraints. in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik Wiley-V C H Verlag Gmbh, Weinheim., 93(12), 928-936. https://doi.org/10.1002/zamm.201200080
Cović V, Mitrović Z, Rusov S, Obradović A. On the instability of equilibrium position of a mechanical system with singular constraints. in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik. 2013;93(12):928-936. doi:10.1002/zamm.201200080 .
Cović, V., Mitrović, Zoran, Rusov, Srđan, Obradović, Aleksandar, "On the instability of equilibrium position of a mechanical system with singular constraints" in Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 93, no. 12 (2013):928-936, https://doi.org/10.1002/zamm.201200080 . .