On the instability of steady motion
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2011
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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.
Ključne reči:
Truncated equations / Kozlov's generalization of the first Lyapunov's method / Instability of steady motions / Gyroscopic forcesIzvor:
Meccanica, 2011, 46, 4, 855-863Izdavač:
- Springer, Dordrecht
Finansiranje / projekti:
- Savremeni problemi mehanike deformabilnog tela (RS-MESTD-MPN2006-2010-144019)
- Razvoj mašina visokih performansi i metoda za identifikaciju njihovog odziva na unutrašnje i spoljašnje poremećaje (RS-MESTD-MPN2006-2010-14052)
DOI: 10.1007/s11012-010-9348-2
ISSN: 0025-6455