 | | 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
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 38, Issue 3 / 2003 | Next article >> |
| S. E. Perelyaev, "3D parametrization of the rigid body rotation group in systems of gyroscopic orientation," Mech. Solids. 38 (3), 12-21 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
3 |
Pages |
12-21 |
| Title |
3D parametrization of the rigid body rotation group in systems of gyroscopic orientation |
| Author(s) |
S. E. Perelyaev (Moscow) |
| Abstract |
Basic methods of the introduction of a local (3D) parametrization
of the configuration space of a rigid body with a fixed point (SO(3))
are described and specific features of these methods are characterized.
These methods of 3D parametrization can be utilized for solving a number
of applied problems of dynamics of a rigid body. Apart from the well-known
methods of local parametrization involving three angles
(Eulerian or Euler-Krylov angles),
we consider also the exponential parametrization. Advantages of Cayley's
linear-fractional parametrization as applied to the solution
of the problem of local parametrization of the group SO(3)
are discussed and analyzed. It is shown that Cayley's 3D parametrization
leads to a Riccati-type kinematic equation, which has a nondegenerate
structure. We consider examples of local coordinates based on Rodrigues
and Gibbs vectors and the kinematic equations represented in terms
of these 3D variables. |
| References |
| 1. | V. Ph. Zhuravlev, Fundamentals of Theoretical Mechanics
[in Russian], Nauka, Moscow, 1997. |
| 2. | J. Stuelpnagel, "On the parametrization of the three-dimensional
rotation group," SIAM Review, Vol. 6, No. 4, pp. 422-429, 1964. |
| 3. | S. N. Kirpichnikov and V. S. Novoselov,
Mathematical Aspects of Rigid Body Kinematics: A Textbook
[in Russian], Izd-vo LGU, Leningrad, 1986. |
| 4. | G. Goldstein, Classical Mechanics [Russian translation],
Gostekhizdat, Moscow, 1957. |
| 5. | E. T. Whittaker, Analytical Dynamics [Russian translation],
ONTI, Moscow, Leningrad, 1937. |
| 6. | J. L. Synge, Classical Dynamics [Russian translation],
Fizmatgiz, Moscow, 1963. |
| 7. | A. Yu. Ishlinskii, Orientation, Gyroscopes, and Inertial
Navigation [in Russian], Nauka, Moscow, 1976. |
| 8. | A. I. Lur'e, Analytical Mechanics [in Russian],
Fizmatlit, Moscow, 1961. |
| 9. | V. I. Smirnov, A Course in Higher Mathematics. Volume 3. Part 1
[in Russian], Fizmatlit, Moscow, 1958. |
| 10. | S. M. Onishchenko, Application of Hyper-complex Numbers in the
Theory of Inertial Navigation [in Russian],
Naukova Dumka, Kiev, 1983. |
| 11. | A. H. Lipton, Alignment of Inertial Systems on a Moving
Base [Russian translation], Nauka, Moscow, 1971. |
| 12. | B. N. Branets and I. P. Shmyglevskii, Introduction
to the Theory of Strapdown Inertial Navigation Systems [in Russian],
Nauka, Moscow, 1992. |
| 13. | S. A. Gorbatenko, E. M. Makashov, Yu. F. Polushkin, and
L. V. Sheftel', Flight Mechanics (General Information. Equations of Motion):
A Handbook for Engineers [in Russian],
Mashinostroenie, Moscow, 1969. |
| 14. | H. J. Marcelo and D. T. Vassilios,
"Singularities of Euler and roll-pitch-yaw representations,"
IEEE Transactions on Aerospace and Electronic Systems,
Vol. 19, No. 1, pp. 59-69, 1987. |
| 15. | A. P. Panov, Mathematical Foundation of Inertial Orientation
[in Russian], Naukova Dumka, Kiev, 1995. |
| 16. | J. E. Bortz, "A new mathematical formulation for strapdown
inertial navigation,"
IEEE Transactions on Aerospace and Electronic Systems,
Vol. AES-7, No. 1, pp. 61-66, 1971. |
| 17. | F. R. Gantmakher, Theory of Matrices [in Russian],
Nauka, Moscow, 1967. |
| 18. | Litton Space Operations. Technology and Product Overview.
May, 1996. |
| 19. | R. Penrose and W. Rindler,
Spinors and Space-time [Russian translation],
Mir, Moscow, 1987. |
| 20. | S. E. Perelyaev, "A new combined algorithm
for determining the orientation of a rigid body,"
Izv. AN. MTT [Mechanics of Solids],
No. 1, pp. 3-19, 2000. |
| 21. | P. G. Savage, "Strapdown system algorithms,"
in ACARD. Advances in Strapdown Inertial Systems,
pp. 3.1-3.28, 1984. |
| 22. | G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists
and Engineers [Russian translation], Nauka, Moscow, 1977. |
| 23. | R. Troilo, "Some theorems on precession motion
and regular precession," in Mechanics. A Periodical Issue
of Translated Papers, No. 5 [Russian translation from Italian], Mir,
Moscow, 1973. |
|
| Received |
20 March 2001 |
| << Previous article | Volume 38, Issue 3 / 2003 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English