 | | 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
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| In English (Mech. Solids): | | 3212 |
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| Yu.N. Chelnokov, "Equations and Algorithms for Determining the Inertial Attitude and Apparent Velocity of a Moving Object in Quaternion and Biquaternion 4D Orthogonal Operators," Mech. Solids. 51 (2), 148-155 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
2 |
Pages |
148-155 |
| DOI |
10.3103/S0025654416020023 |
| Title |
Equations and Algorithms for Determining the Inertial Attitude and Apparent Velocity of a Moving Object in Quaternion and Biquaternion 4D Orthogonal Operators |
| Author(s) |
Yu.N. Chelnokov (Institute for Precision Mechanics and Control Problems, Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia; Chernyshevskii Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia, chelnokovyun@gmail.com) |
| Abstract |
We consider equations and algorithms describing the operation of strapdown inertial navigation systems (SINS) intended for determining the inertial attitude parameters (the Rodrigues-Hamilton (Euler) parameters) and the apparent velocity of a moving object. The construction of these equations and algorithms is based on the Kotelnikov-Study transference principle, Hamiltonian quaternions and Clifford biquaternions, and differential equations in four-dimensional (quaternion and biquaternion) orthogonal operators. |
| Keywords |
moving object, real and dual Rodrigues-Hamilton (Euler) parameters, inertial attitude, apparent velocity, Kotelnikov-Study transference principle, Hamiltonian quaternions, Clifford biquaternions |
| References |
| 1. | Yu. N. Chelnokov,
Quaternion and Biquaternion Models and Methods of Mechanics of Solids and Their Applications. Geometry and Kinematics of Motion
(Fizmatlit, Moscow, 2006)
[in Russian]. |
| 2. | Yu. N. Chelnokov, L. A. Chelnokova, and S. E. Perelyaev,
"New Equations and Algorithms of SINS Operation Based on
the Kotelnikov-Study Superposition and Transference Principles,"
in Proc. 17th Intern. Conf. "System Analysis, Control, and Navigation"
(Izdat. MAI, Moscow, 2012),
pp. 49-51
[in Russian]. |
| 3. | Yu. N. Chelnokov,
"Kotelnikov-Study Superposition and Transference Principles in Inertial Navigation and Motion Control,"
in Proc. 18th Intern. Conf. "System Analysis, Control, and Navigation"
(Izdat. MAI, Moscow, 2013),
pp. 124-126
[in Russian]. |
| 4. | Yu. N. Chelnokov and S. E. Perelyaev, "New Equations and
Algorithms of SINS Operation Constructed Using the
Kotelnikov-Study Superposition and Transference Principles," in
in Proc. XXth St. Petersburg Intern. Conf. on Integrated Navigation Systems (State Scientific Center of the Russian Federation, OOO "Concern 'TsNII Elektropribor'," St. Petersburg,
2013), pp. 54-57 [in Russian]. |
| 5. | Yu. N. Chelnokov, "One Form of the Inertial Navigation
Equations," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 20-28
(1981) [Mech. Solids (Engl. Transl.)]. |
| 6. | Yu. N. Chelnokov,
"On Integration of Kinematic Equations of a Rigid Body's Screw-Motion,"
Prikl. Mat. Mekh.
44 (1), 32-39 (1980)
[J. Appl. Math. Mech. (Engl. Transl.)
44 (1), 19-23 (1980)]. |
| 7. | Yu. N. Chelnokov,
"On Stability of Solutions to Biquaternion Kinematic Equations of Helical Motion of Solids,"
in Collection of Sci.-Method. Papers on Theor. Mech., No. 13
(Vysshaya Shkola, Moscow, 1983),
pp. 103-109
[in Russian]. |
| 8. | Yu. N. Chelnokov,
"Inertial Navigation Equations for the Apparent and Gravitational Velocities
and Their Analytic Solutions for an Immovable Object,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 6-18 (2016)
[Mech. Solids (Engl. Transl.)
51 (1), 1-11 (2016)]. |
| 9. | V. N. Branets and I. P. Shmyglevskii,
Introduction to the Theory of Strapdown Inertial Navigation Systems
(Nauka, Moscow, 1992)
[in Russian]. |
| 10. | A. P. Kotelnikov,
Helical Calculus and Some of Its Applications to Geometry and Mechanics
(Kazan, 1895)
[in Russian]. |
| 11. | A. P. Kotelnikov,
"Screws and Complex Numbers,"
Izv. Fiz.-Mat. Obshch. Imper. Kazan. Univ. Ser. 2,
No. 6, 23-33 (1896). |
| 12. | A. P. Kotelnikov,
"Theory of Vectors and Complex Numbers,"
in Several Applications of Lobachevskii's Ideas in Mechanics and Physics, Collection of Papers
(Gostekhizdat, Moscow, 1950),
pp. 7-47
[in Russian]. |
| 13. | F. M. Dimentberg,
Theory of Screws and Its Applications
(Nauka, Moscow, 1978)
[in Russian]. |
| 14. | A. Edvards,
"Strapdown Inertial Navigation Systems,"
Vopr. Raketn. Tekhn.,
No. 5, 50-57 (1973). |
| 15. | P. N. Besarab, "Determination of the Spatial Attitude Parameters
of a Moving Object," Zh. Vychisl. Mat. Mat. Fiz. 14 (1),
240-246 (1974) [USSR Comput. Math. Math. Phys. (Engl. Transl.)
14 (1), 242-248 (1974)]. |
| 16. | V. N. Branets,
Lectures on the Theory of Strapdown Inertial Navigation Systems
(MFTI, Moscow, 2009)
[in Russian]. |
| 17. | A. P. Panov, Mathematical Foundations of the Theory of Inertial Attitude (Naukova Dumka, Kiev, 1995) [in Russian]. |
|
| Received |
14 November 2013 |
| Link to Fulltext |
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