 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| 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. |
| References |
| 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 |
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