 | | 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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| A. P. Markeev, "Stability of a periodic motion of a rod suspended by an ideal thread," Mech. Solids. 42 (4), 497-506 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
4 |
Pages |
497-506 |
| Title |
Stability of a periodic motion of a rod suspended by an ideal thread |
| Author(s) |
A. P. Markeev (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, markeev@ipmnet.ru) |
| Abstract |
We consider the plane motion of a rod suspended by an ideal thread in a homogeneous field of gravity. We study the nonlinear orbital stability problem for the translational periodic motion of the rod along the vertical. Depending on two dimensionless parameters of the problem, we make conclusions on orbital instability, stability for a majority of initial conditions, or formal stability. |
| References |
| 1. | A. P. Markeev, "Studying the Stability of Periodic Motion of a
Rigid Body in the Presence of Impacts against the Horizontal
Plane," Prikl. Mat. Mekh. 58 (3), 71-81 (1994) [J. Appl.
Math. Mech. (Engl. Transl.)]. |
| 2. | A. P. Markeev, "On Vibrations of a Material Point Suspended by an
Ideal Thread," Prikl. Mat. Mekh. 60 (2), 240-249 (1996)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 3. | P. Appell,
Theoretical Mechanics, Vol. 2
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[in Russian]. |
| 4. | A. P. Markeev,
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| 5. | E. T. Whitteker,
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[in Russian]. |
| 6. | I. G. Malkin,
Theory of Motion Stability
(Nauka, Moscow, 1966)
[in Russian]. |
| 7. | A. M. Lyapunov,
"On Stability of Motion in a Special Case of the Three-Body Problem,"
in Collected Works
(Izd-vo AN SSSR, Moscow-Leningrad, 1954)
Vol. 1, pp. 327-401
[in Russian]. |
| 8. | A. P. Markeev,
"Constructive Algorithm for Normalization of a Periodic Hamiltonian,"
Prikl. Mat. Mekh.
69 (3), 355-371 (2005)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 9. | V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt,
Mathematical Aspects of Classical and Celestial Mechanics
(Springer-Verlag, New York, 1988; Editorial URSS, Moscow, 2002). |
| 10. | J. Moser,
Lectures on Hamiltonian Systems
(Mir, Moscow, 1973)
[in Russian]. |
| 11. | A. P. Markeev,
Libration Points in Celestial Mechanics and Space Dynamics
(Nauka, Moscow, 1978)
[in Russian]. |
| 12. | V. I. Arnold,
Mathematical Methods of Classical Mechanics
(Nauka, Moscow, 1979)
[in Russian]. |
| 13. | J. Moser,
"New Aspects in the Theory of Stability of Hamiltonian Systems,"
Comm. Pure Appl. Math.
11 (1), 81-114 (1958). |
| 14. | J. Glimm,
"Formal Stability of Hamiltonian Systems,"
Comm. Pure Appl. Math.
17 (4), 509-526 (1964). |
|
| Received |
29 March 2005 |
| Link to Fulltext |
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