Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces
Abstract
The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative, conservative, and circulatory forces. The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity. It is assumed that the kinetic energy, the Rayleigh dissipation function, and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained here are partially generalized the results obtained by Kozlov et al. (Kozlov, V. V. The asymptotic motions of systems with dissipation. Journal of Applied Mathematics and Mechanics, 58(5), 787-792 (1994). Merkin, D. R. Introduction to the Theory of the Stability of Motion (in Russian), Nauka, Moscow (1987). Thomson, W. and Tait, P. Treatise on Natural Philosophy, Part I, Cambridge University Press, Cambridge (1879)). The results are... illustrated by an example.
Keywords:
potential / nonholonomic constraint / instability / dissipative forceSource:
Applied Mathematics and Mechanics-English Edition, 2011, 32, 2, 211-222Publisher:
- SHANGHAI UNIV, SHANGHAI
Funding / projects:
- Mechanics of nonlinear and dissipative systems - contemporary models, analysis and applications (RS-MESTD-Basic Research (BR or ON)-174016)
- 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: 10.1007/s10483-011-1407-9
ISSN: 0253-4827
WoS: 000286938700008
Scopus: 2-s2.0-79551655710
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Vesković, M. AU - Cović, V. AU - Obradović, Aleksandar PY - 2011 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1154 AB - The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative, conservative, and circulatory forces. The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity. It is assumed that the kinetic energy, the Rayleigh dissipation function, and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained here are partially generalized the results obtained by Kozlov et al. (Kozlov, V. V. The asymptotic motions of systems with dissipation. Journal of Applied Mathematics and Mechanics, 58(5), 787-792 (1994). Merkin, D. R. Introduction to the Theory of the Stability of Motion (in Russian), Nauka, Moscow (1987). Thomson, W. and Tait, P. Treatise on Natural Philosophy, Part I, Cambridge University Press, Cambridge (1879)). The results are illustrated by an example. PB - SHANGHAI UNIV, SHANGHAI T2 - Applied Mathematics and Mechanics-English Edition T1 - Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces EP - 222 IS - 2 SP - 211 VL - 32 DO - 10.1007/s10483-011-1407-9 ER -
@article{ author = "Vesković, M. and Cović, V. and Obradović, Aleksandar", year = "2011", abstract = "The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative, conservative, and circulatory forces. The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity. It is assumed that the kinetic energy, the Rayleigh dissipation function, and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained here are partially generalized the results obtained by Kozlov et al. (Kozlov, V. V. The asymptotic motions of systems with dissipation. Journal of Applied Mathematics and Mechanics, 58(5), 787-792 (1994). Merkin, D. R. Introduction to the Theory of the Stability of Motion (in Russian), Nauka, Moscow (1987). Thomson, W. and Tait, P. Treatise on Natural Philosophy, Part I, Cambridge University Press, Cambridge (1879)). The results are illustrated by an example.", publisher = "SHANGHAI UNIV, SHANGHAI", journal = "Applied Mathematics and Mechanics-English Edition", title = "Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces", pages = "222-211", number = "2", volume = "32", doi = "10.1007/s10483-011-1407-9" }
Vesković, M., Cović, V.,& Obradović, A.. (2011). Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces. in Applied Mathematics and Mechanics-English Edition SHANGHAI UNIV, SHANGHAI., 32(2), 211-222. https://doi.org/10.1007/s10483-011-1407-9
Vesković M, Cović V, Obradović A. Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces. in Applied Mathematics and Mechanics-English Edition. 2011;32(2):211-222. doi:10.1007/s10483-011-1407-9 .
Vesković, M., Cović, V., Obradović, Aleksandar, "Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces" in Applied Mathematics and Mechanics-English Edition, 32, no. 2 (2011):211-222, https://doi.org/10.1007/s10483-011-1407-9 . .