 | | 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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| << Previous article | Volume 41, Issue 4 / 2006 | Next article >> |
| N. I. Amel'kin, "On the motions of a rigid body containing two-degree-of-freedom control moment gyros with dissipation in gimbal axes," Mech. Solids. 41 (4), 12-20 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
4 |
Pages |
12-20 |
| Title |
On the motions of a rigid body containing two-degree-of-freedom control moment gyros with dissipation in gimbal axes |
| Author(s) |
N. I. Amel'kin (Moscow) |
| Abstract |
We consider a system that consists of a supporting rigid body and
two-degree-of-freedom gyros and is not a gyrostat in general. The equations
of motion of the system under the action of arbitrary forces are derived.
The case in which external couples are absent and only dissipative and
potential torques act in the gimbal axes is considered. We show that the
limit motions of the system are equilibrium motions in which the gyro
gimbals do not move relative to the support. Differential equations for
equilibrium motions and algebraic equations for steady motions are
obtained. We find an auxiliary function V (the total energy calculated
for "frozen" rotors) that does not increase along motions of the system
and prove a theorem on the correspondence between steady motions and
stationary points of V on the manifold determined by the angular momentum
integral of the system. We discuss a method for stability analysis of
steady motions in which V is used as a Lyapunov function.
The results are generalized to the problem on the motion of a system of
rigid bodies connected by hinged joints. |
| References |
| 1. | B. V. Raushenbakh and E. N. Tokar', Control of Spacecraft
Orientation [in Russian], Nauka, Moscow, 1974. |
| 2. | E. N. Tokar', "Problems of control of CMG balancers," Kosmicheskie
Issledovaniya, Vol. 16, No. 2, pp. 179-187, 1978. |
| 3. | V. A. Sarychev,
"Problems of orientation of artificial Earth satellites,"
in Itogi Nauki i Tekhniki, Ser. Space Studies, VINITI, Vol. 11, 1978. |
| 4. | S. A. Mirer, "Optimal gyro damping of nutational oscillations of
a satellite stabilized by rotation," Kosmicheskie Issledovaniya, Vol. 15,
No. 5, pp. 677-682, 1977. |
| 5. | V. A. Sarychev, S. A. Mirer, and A. V. Isakov, "Gyro damper on a
satellite with double rotation," Kosmicheskie Issledovaniya, Vol. 20, No. 1,
pp. 30-40, 1982. |
| 6. | E. A. Barbashin,
Introduction to Stability Theory [in Russian],
Nauka, Moscow, 1967. |
| 7. | N. Rouché, P. Habets, and M. Laloy, Stability Theory by
Liapunov's Direct Method, Springer, Berlin, 1977. |
| 8. | A. V. Karapetyan,
Stability of Steady Motions [in Russian], Editorial URSS, Moscow, 1998. |
|
| Received |
10 June 2004 |
| << Previous article | Volume 41, Issue 4 / 2006 | Next article >> |
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