 | | 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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| Yu.N. Chelnokov, "Inertial Navigation Equations for the Apparent and Gravitational Velocities and Their Analytic Solutions for an Immovable Object," Mech. Solids. 51 (1), 1-11 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
1 |
Pages |
1-11 |
| DOI |
10.3103/S0025654416010015 |
| Title |
Inertial Navigation Equations for the Apparent and Gravitational Velocities and Their Analytic Solutions for an Immovable Object |
| 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 propose new differential equations describing the perfect operation of strapdown intertial navigation systems (SINS) intended to determine the apparent, gravitational, and relative velocities of a moving object and the geographic coordinates of the object position. The superposition principle is used to construct the equations.
We construct analytical solutions of differential equations for the apparent and gravitational velocities in the case of an object immovable with respect to the Earth, which can be used to analyze the accuracy of operation of SINS mounted on an immovable base. |
| Keywords |
moving object, apparent, gravitational, and relative velocities, geographic coordinates, superposition principle, analytic solutions |
| References |
| 1. | 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]. |
| 2. | 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]. |
| 3. | Yu. N. Chelnokov and S. E. Perelyaev,
"New Equations and Algorithms of SINS Operation Constructed Using
the Kotelnikov-Study superposition and transference principles,"
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]. |
| 4. | 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]. |
| 5. | 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]. |
| 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,
"One Form of the Equations of Inertial Navigation,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 5, 20-28 (1981)
[Mech. Solids (Engl. Transl.)]. |
| 8. | V. N. Branets and I. P. Shmyglevskii,
Introduction to the Theory of Strapdown Inertial Navigation Systems
(Nauka, Moscow, 1992)
[in Russian]. |
| 9. | V. N. Branets and I. P. Shmyglevskii,
Application of Quaternions in Problems of Orientation of a Rigid Body
(Nauka, Moscow, 1973)
[in Russian]. |
| 10. | A. Yu. Ishlinskii,
Orientation, Gyroscopes, and Inertial Navigation
(Nauka, Moscow, 1976)
[in Russian]. |
| 11. | D. M. Klimov,
Inertial Navigation on the Sea
(Nauka, Moscow, 1984)
[in Russian]. |
| 12. | V. Ph. Zhuravlev,
Foundations of Theoretical Mechanics
(Nauka, Moscow, 2008)
[in Russian]. |
| 13. | A. P. Kotelnikov,
Helical Calculus and Some of Its Applications to Geometry and Mechanics
(Kazan, 1895)
[in Russian]. |
| 14. | A. P. Kotelnikov,
"Screws and Complex Numbers,"
Izv. Fiz.-Mat. Obshch. Imper. Kazan. Univ. Ser. 2,
No. 6, 23-33 (1896). |
| 15. | 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]. |
| 16. | F. M. Dimentberg,
Theory of Screws and Its Applications
(Nauka, Moscow, 1978)
[in Russian]. |
| 17. | I. Y. Bar-Itzhack,
"Navigation Computation in Terrestrial Strapdown Inertial Navigation Systems,"
IEEE Trans. Aerospace Electr. Syst.
AES-13 (6), 679-689 (1977). |
| 18. | N. T. Kuzovkov and O. S. Silychev,
Inertial Navigation and Optimal Filtration
(Mashinostroenie, Moscow, 1982)
[in Russian]. |
| 19. | A. Yu. Ishlinskii,
Mechanics of Relative Motion and Inertia Forces
(Nauka, Moscow, 1981)
[in Russian]. |
| 20. | P. V. Bronberg,
Theory of Inertial Navigation Systems
(Nauka, Moscow, 1979)
[in Russian]. |
|
| Received |
20 May 2013 |
| Link to Fulltext |
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