Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us

IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2006-4pp.64-72

Archive of Issues

Total articles in the database: 10864
In Russian (. . ): 8009
In English (Mech. Solids): 2855

<< Previous article | Volume 41, Issue 4 / 2006 | Next article >>
I. I. Kosenko and S. Ya. Stepanov, "Stability of relative equilibria of an orbit tether with impact interactions taken into account. The unbounded problem," Mech. Solids. 41 (4), 64-72 (2006)
Year 2006 Volume 41 Number 4 Pages 64-72
Title Stability of relative equilibria of an orbit tether with impact interactions taken into account. The unbounded problem
Author(s) I. I. Kosenko (Moscow)
S. Ya. Stepanov (Moscow)
Abstract We completely solve the 3D problem on the stability of relative equilibria of an orbit tether. The problem is considered in the unbounded setting. We assume that the material points constituting the tether are connected by a flexible weightless inextensible cable and each of them independently performs a Kepler motion interrupted from time to time by the constraint, which is implemented as a flexible inextensible weightless cable of constant length.

We use Routh reduction and calculate the relative equilibria corresponding to the radial position of the cable. We verify the condition that the constraint is in tension and the assumptions of A. P. Ivanov's theorem on the stability of the equilibrium of a Lagrangian mechanical system with unilateral constraints.
1.  V. I. Arnold, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow, 1979.
2.  E. T. Whittaker, Analytical Dynamics [in Russian], Udmurtsk. Un-t, Izhevsk, 1999.
3.  A. P. Ivanov, "On stability in systems with unilateral constraints," PMM [Applied Mathematics and Mechanics], Vol. 48, No. 5, pp. 725-732, 1984.
4.  Li-Sheng Wang and Shyh-Feng Cheng, "Dynamics of two spring-connected masses in orbit," Celest. Mech. and Dynam. Astronomy, Vol. 63, nos. 3-4, pp. 289-312, 1996.
5.  V. V. Beletskii, Essays on Motion of Space Bodies [in Russian], Nauka, Moscow, 1977.
6.  V. V. Beletskii and E. M. Levin, Dynamics of Space Cable Systems [in Russian], Nauka, Moscow, 1990.
7.  V. V. Beletskii and O. N. Ponomarev, "Parametric analysis of stability of relative equilibria in gravitational field," Kocmich. Issledovaniya, Vol. 28, No. 5, pp. 664-675, 1990.
8.  M. Krupa, A. Steindl, and H. Troger, "Stability of relative equilibria, Pt. 2, Dumb-bell satellites," Meccanica, Vol. 35, No. 4, pp. 353-371, 2000.
9.  S. Ya. Stepanov, "Conditions for secular and gyroscopic stability of steady-state solutions in the generalized plane three-body problem," in Problems of Studying Stability and Motion Stabilization [in Russian], pp. 33-44, Moscow, VTs RAN, 1999.
10.  V. V. Kozlov and D. V. Treshchev, Billiards. Genetic Introduction to Dynamics of Systems with Impacts [in Russian], Moscow, Izd-vo MGU, 1991.
11.  A. A. Burov, "On the Routh method for mechanical systems subjected to unilateral constraints," in Progr. Nonlinear Science: Proc. Intern. Conf. Dedicated to the 100th Anniversary of A. A. Andronov. Volume I. Mathematical Problems of Nonlinear Dynamics, pp. 196-201, Nizhegorodsk. Un-t, Nizhny Novgorod, 2002.
Received 01 August 2004
<< Previous article | Volume 41, Issue 4 / 2006 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
Rambler's Top100