 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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| V. N. Koshlyakov and V. A. Storozhenko, "The influence of the dissipation on the stability of the rotation of a rigid body suspended on a rod," Mech. Solids. 40 (3), 16-25 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
3 |
Pages |
16-25 |
| Title |
The influence of the dissipation on the stability of the rotation of a rigid body suspended on a rod |
| Author(s) |
V. N. Koshlyakov (Kiev)
V. A. Storozhenko (Kiev) |
| Abstract |
The investigation of the influence of resistance forces on the dynamics of mechanical systems is a
rather topical issue. This investigation is frequently complicated by the feature that taking into
account the resistance forces leads to the appearance in the perturbed equations of motion not only
of dissipative terms depending on the generalized velocities but also nonpotential positional
forces depending on the generalized coordinates. The latter forces create certain difficulties,
since the methods of analysis of such systems have been developed insufficiently thoroughly. The
stability problem for two-degree-of-freedom mechanical systems of such a type was considered in [1,
2]. In [3, 7], for systems governed by general $n$th-order equations, the problem of reduction of
these equations to the form convenient for the application of the familiar Thomson-Tait-Chetaev
theorems [7] was solved. The analytical techniques of the cited publications turned out to be
especially effective for the investigation of the dynamics of symmetric mechanical
systems, in particular for the stability analysis of
rotation of a rigid body suspended on a rod (string). |
| References |
| 1. | A. Yu. Ishlinskii, V. A. Storozhenko, and M. E. Temchenko,
"On the influence of external an internal friction on the stability
of the vertical rotation of a rigid body,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 12-22, 1995. |
| 2. | V. A. Storozhenko, "On the influence of nonpotential positional
forces in systems with rotation,"
Dop. NAN Ukrainy. Ser. Matem., Prir., Tekhn. Nauki, No. 7, pp. 67-70, 1998. |
| 3. | P. C. Müller, Stabilität und Matrizen, Springer, Berlin, New York, 1977. |
| 4. | V. N. Koshlyakov, "On structural transformations of nonconservative
systems," PMM [Applied Mathematics and Mechanics], Vol. 64, No. 6, pp. 933-941, 2000. |
| 5. | V. N. Koshlyakov and V. L. Makarov, "Structural analysis of a class of dynamic systems,"
Ukr. Mat. Zh., Vol. 52, No. 8, pp. 1089-1096, 2000. |
| 6. | V. N. Koshlyakov and V. L. Makarov,
"To the theory of gyroscopic systems with nonpotential forces,"
PMM [Applied Mathematics and Mechanics], Vol. 65, No. 4, pp. 698-704, 2001. |
| 7. | D. R. Merkin, Gyroscopic Systems, Nauka, Moscow, 1974. |
| 8. | V. V. Bolotin, Nonconservative Problems of the Theory of Elastic Stability [in Russian],
Fizmatgiz, Moscow, 1961. |
| 9. | A. Yu. Ishlinskii, V. A. Storozhenko, and M. E. Temchenko,
Rotation of a Rigid Body on a String and Related Problems
[in Russian], Nauka, Moscow, 1991. |
| 10. | Yu. A. Krutkov, "On a special case of Brownian rotating motion," Doklady AN SSSR,
Vol. 3, No. 3, pp. 153-159, 1934. |
| 11. | Yu. A. Krutkov, "Brownian rotating motion of a particle
with an axis of symmetry,"
Doklady AN SSSR, Vol. 1, No. 6, pp. 366-371, 1935. |
| 12. | A. V. Karapetyan and I. S. Lagutina, "Stability of uniform rotations of a top suspended
on a string and subjected to dissipative and constant torques," Izv. AN. MTT [Mechanics of
Solids], No. 1, pp. 53-57, 2000. |
|
| Received |
09 February 2004 |
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