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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
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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.
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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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