On the instability of steady motion
Само за регистроване кориснике
2011
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
This paper deals with the instability of steady motions of conservative mechanical systems with cyclic coordinates. The following are applied: Kozlov's generalization of the first Lyapunov's method, as well as Rout's method of ignoration of cyclic coordinates. Having obtained through analysis the Maclaurin's series for the coefficients of the metric tensor, a theorem on instability is formulated which, together with the theorem formulated in Furta (J. Appl. Math. Mech. 50(6):938-944, 1986), contributes to solving the problem of inversion of the Lagrange-Dirichlet theorem for steady motions. The cases in which truncated equations involve the gyroscopic forces are solved, too. The algebraic equations resulting from Kozlov's generalizations of the first Lyapunov's method are formulated in a form including one variable less than was the case in existing literature.
Кључне речи:
Truncated equations / Kozlov's generalization of the first Lyapunov's method / Instability of steady motions / Gyroscopic forcesИзвор:
Meccanica, 2011, 46, 4, 855-863Издавач:
- Springer, Dordrecht
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/s11012-010-9348-2
ISSN: 0025-6455
WoS: 000292567500017
Scopus: 2-s2.0-79961028734
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Cović, V. AU - Vesković, M. AU - Obradović, Aleksandar PY - 2011 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1210 AB - This paper deals with the instability of steady motions of conservative mechanical systems with cyclic coordinates. The following are applied: Kozlov's generalization of the first Lyapunov's method, as well as Rout's method of ignoration of cyclic coordinates. Having obtained through analysis the Maclaurin's series for the coefficients of the metric tensor, a theorem on instability is formulated which, together with the theorem formulated in Furta (J. Appl. Math. Mech. 50(6):938-944, 1986), contributes to solving the problem of inversion of the Lagrange-Dirichlet theorem for steady motions. The cases in which truncated equations involve the gyroscopic forces are solved, too. The algebraic equations resulting from Kozlov's generalizations of the first Lyapunov's method are formulated in a form including one variable less than was the case in existing literature. PB - Springer, Dordrecht T2 - Meccanica T1 - On the instability of steady motion EP - 863 IS - 4 SP - 855 VL - 46 DO - 10.1007/s11012-010-9348-2 ER -
@article{ author = "Cović, V. and Vesković, M. and Obradović, Aleksandar", year = "2011", abstract = "This paper deals with the instability of steady motions of conservative mechanical systems with cyclic coordinates. The following are applied: Kozlov's generalization of the first Lyapunov's method, as well as Rout's method of ignoration of cyclic coordinates. Having obtained through analysis the Maclaurin's series for the coefficients of the metric tensor, a theorem on instability is formulated which, together with the theorem formulated in Furta (J. Appl. Math. Mech. 50(6):938-944, 1986), contributes to solving the problem of inversion of the Lagrange-Dirichlet theorem for steady motions. The cases in which truncated equations involve the gyroscopic forces are solved, too. The algebraic equations resulting from Kozlov's generalizations of the first Lyapunov's method are formulated in a form including one variable less than was the case in existing literature.", publisher = "Springer, Dordrecht", journal = "Meccanica", title = "On the instability of steady motion", pages = "863-855", number = "4", volume = "46", doi = "10.1007/s11012-010-9348-2" }
Cović, V., Vesković, M.,& Obradović, A.. (2011). On the instability of steady motion. in Meccanica Springer, Dordrecht., 46(4), 855-863. https://doi.org/10.1007/s11012-010-9348-2
Cović V, Vesković M, Obradović A. On the instability of steady motion. in Meccanica. 2011;46(4):855-863. doi:10.1007/s11012-010-9348-2 .
Cović, V., Vesković, M., Obradović, Aleksandar, "On the instability of steady motion" in Meccanica, 46, no. 4 (2011):855-863, https://doi.org/10.1007/s11012-010-9348-2 . .