On the instability of steady motion |
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Authors: | V Čović M Vesković A Obradović |
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Institution: | 1.Faculty of Mechanical Engineering,University of Belgrade,Belgrade,Serbia;2.Faculty of Mechanical Engineering,University of Kragujevac,Kraljevo,Serbia |
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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. |
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Keywords: | |
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