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1998 Influence of dissipative forces on the stability behavior of the steady motions of Lagrangian mechanical systems with cyclic coordinates
Stephen R. Bernfeld, Luigi Salvadori, Francesca Visentin
Differential Integral Equations 11(6): 807-822 (1998).

Abstract

We are concerned with stability problems for a holonomic system $\mathcal {S}$ with $n$ degrees of freedom having $n-m$ cyclic coordinates, $m<n$. Let $x$ be the set of the acyclic coordinates and let $v$ be the set of the generalized velocities corresponding to the cyclic coordinates. For $\mathcal {S}$ conservative or subject to a dissipation restricted to the acyclic coordinates, we revisit classical stability results concerning the steady motions of the system and give some new contribution. When $\mathcal {S}$ is strictly dissipative with respect to all the coordinates, the integrals of momenta disappear and so do the steady motions. In this case, under suitable conditions there exist motions for which $x$ is constant and, consequently, $v \rightarrow 0$ as $t \rightarrow +\infty$ (pseudosteady motions). We analyze the stability properties with respect to $(x, \dot x)$ of these motions. Such properties define a stable or unstable behavior with respect to $(x, \dot x)$ of corresponding steady motions of the conservative system under the influence of strictly dissipative perturbing

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Stephen R. Bernfeld. Luigi Salvadori. Francesca Visentin. "Influence of dissipative forces on the stability behavior of the steady motions of Lagrangian mechanical systems with cyclic coordinates." Differential Integral Equations 11 (6) 807 - 822, 1998.

Information

Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1015.34045
MathSciNet: MR1659272

Subjects:
Primary: 34D20
Secondary: 37C75, 70F20, 70K20

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 6 • 1998
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