 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| K. G. Petrov and A. A. Tikhonov, "Equations of rotary motion of a rigid body based on the utilization of quaternion parameters," Mech. Solids. 37 (3), 1-12 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
1-12 |
| Title |
Equations of rotary motion of a rigid body based on the utilization of quaternion parameters |
| Author(s) |
K. G. Petrov (St. Petersburg)
A. A. Tikhonov (St. Petersburg) |
| Abstract |
Four modifications of equations of rotary motion of a rigid body
allowing the separation of variables into slow and fast ones are
constructed. These equations are similar to Beletskii-Chernousko
equations. Unlike the latter equations, the equations constructed
in the present paper utilize
Rodrigues-Hamilton parameters and s-parameters (modified
Rodrigues-Hamilton parameters) instead of Eulerian angles.
These equations can be used for both analytical and numerical
investigation of the rotary motion. For the numerical
analysis, the equations constructed should be preferred to
Beletskii-Chernousko equations for that reason that they
do not contain trigonometric functions and singularities associated
with the fast variables and, in addition, two of the systems constructed
do not contain trigonometric functions and singularities associated
with the slow variables. It is established that, in contrast to
the common opinion that s-parameters are suitable for the
description of only libration motions and rotations by small angles,
these variables are also quite applicable for the description
of the rotary motion of the body. |
| References |
| 1. | Yu. G. Martynenko, "Spinning up of a gyro with contactless
suspension of the rotor,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 35-40, 1973. |
| 2. | V. Ph. Zhuravlev, "On one form of the equations of motion
of a symmetric rigid body,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 3, pp. 5-11, 1986. |
| 3. | V. V. Beletskii, V. V. Golubkov, E. A. Stepanova,
and I. G. Khatskevich, The Determination of the Orientation
of Satellites by Measurement Data. Part 1: Method. Part 2: Results [in
Russian], Preprint, Institute of Applied Mathematics of the USSR Academy of
Sciences, Moscow, 1967, 1968. |
| 4. | V. V. Beletskii, V. V. Golubkov, E. K. Lavrovskii,
S. I. Trushin, and I. G. Khatskevich,
"The determination of the orientation and rotation of satellites
by measurement data," Kosmicheskie Issledovaniya [Cosmic Research],
Vol. 5, No. 5, pp. 686-702, 1967. |
| 5. | V. V. Golubkov, and I. G. Khatskevich,
"The determination of the orientation of earth satellites
by a prescribed system of measurements," Kosmicheskie Issledovaniya [Cosmic
Research], Vol. 7, No. 4, pp. 510-521, 1969. |
| 6. | V. V. Beletskii, V. V. Golubkov, E. A. Stepanova,
and I. G. Khatskevich, "The results of the determination
of the orientation of the satellite "Proton" and
the description of its attitude motion,"
Kosmicheskie Issledovaniya [Cosmic Research],
Vol. 7, No. 4, pp. 522-533, 1969. |
| 7. | V. V. Beletskii, "Estimation of the character of the interaction
of an aerodynamic flow with a satellite on the basis of the analysis
of the motion of the satellite,"
Kosmicheskie Issledovaniya [Cosmic Research],
Vol. 8, No. 2, pp. 206-217, 1970. |
| 8. | A. A. Tikhonov, "On the equations of the attitude motion
of an electrically charged body in the geomagnetic field,"
Vestnik SPbGU, Ser. 1, No. 3 (15),
pp. 83-87, 1990. |
| 9. | S. R. Marandi and V. J. Modi, "A preferred coordinate system
and the associated orientation representation in attitude dynamics,"
Acta Astronaut., Vol. 15, No. 11, pp. 833-843, 1987. |
| 10. | V. V. Beletskii, "The Motion of a Satellite about the Center
of Mass in the Gravitational Field [in Russian],
Izd-vo MGU, Moscow, 1975. |
| 11. | V. N. Branets and I. P. Shmyglevskii, Application of Quaternions
in Problems of Orientation of a Rigid Body [in Russian],
Nauka, Moscow, 1973. |
| 12. | M. D. Shuster, "A survey of attitude representations,"
J. Astronaut. Sci., Vol. 41, No. 4, pp. 439-577, 1993. |
|
| Received |
22 May 2000 |
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