 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 49, Issue 2 / 2014 | Next article >> |
| V.F. Chub, "Exact Thomas Precession Related Solutions of the Inertial Navigation Equations," Mech. Solids. 49 (2), 113-126 (2014) |
| Year |
2014 |
Volume |
49 |
Number |
2 |
Pages |
113-126 |
| DOI |
10.3103/S0025654414020010 |
| Title |
Exact Thomas Precession Related Solutions of the Inertial Navigation Equations |
| Author(s) |
V.F. Chub (Korolev Rocket and Space Corporation "Energia," Lenina 4A, Korolev, Moscow Oblast, 141070 Russia, v.chub@mail.ru) |
| Abstract |
The aim of the present paper is to give a survey of those exact solutions of relativistic inertial navigation equations which are directly or indirectly related to Thomas precession. Various cases of uniform circular motion of an object in gravity-free space close to motion with inertial or orbital attitude are considered. |
| Keywords |
Thomas precession, Poincaré group, quaternion, biquaternion, inertial navigation equations, Gravity Probe B experiment |
| References |
| 1. | A. Yu. Ishlinskii,
Mechanics: Ideas, Problems, Applications
(Nauka, Moscow, 1985)
[in Russian]. |
| 2. | R. Feynman, R. Leighton, and M. Sands,
The Feynman Lectures on Physics,
Vol. 1: Mainly Mechanics, Radiation, and Heat
(Addison-Wesley, Reading, MA, 1963-1965; Mir, Moscow, 1965). |
| 3. | L. I. Sedov,
Basic Models in Mechanics
(Izd-vo MGU, Moscow, 1992)
[in Russian]. |
| 4. | I. D. Blumin,
"Chap. 6. Theory of Inertial Navigation Systems,"
in Progress in General Mechanics in Russia and Ukraine in the 1920-1980s
(Nauka, Moscow, 1998; Feniks, Kiev, 1998),
pp. 148-181
[in Russian]. |
| 5. | M. I. Kaganov,
"The Publication of the Physics Encyclopedia Has Been Completed,"
Uspekhi Fiz. Nauk
169 (11), 1283-1287 (1999)
[Phys. Uspekhi (Engl. Transl.)
42 (11), 1177-1181 (1999)]. |
| 6. | M. M. Kuritsky, M. S. Goldstein, I. A. Greenwood, et al.
"Inertial Navigation,"
Proc. IEEE (Special Edition "Global Navigation Systems"),
Vol. 71 (10), 1156-1176 (1983)
[TIEER (Russ. Transl.)
Vol. 71 (10), 47-74 (1983)]. |
| 7. | "Inertial Navigation,"
in Polytechnical Dictionary
(Sov. Entsiklopediya, 1989)
[in Russian]. |
| 8. | Yu. G. Martynenko,
"Inertial Navigation,"
Soros. Obrazovat. Zh.,
No. 8, 102-108 (1998). |
| 9. | L. A. Dmitrochenko and V. I. Lopatin,
"Specific Features of Algorithms of Strapdown Inertial Navigation Systems,"
in Problems of Spacecraft Control (according to Foreign Materials)
(Mir, Moscow, 1975),
pp. 95-117
[in Russian]. |
| 10. | V. V. Yagodkin,
Strapdown Inertial Navigation Systems
(MVTU, Moscow, 1979)
[in Russian]. |
| 11. | L. A. Dmitrochenko, V. P. Gora, and G. F. Savinov,
Strapdown Inertial Navigation Systems
(MAI, Moscow, 1984)
[in Russian]. |
| 12. | V. N. Branets and I. P. Shmyglevskii,
Introduction to the Theory of Strapdown Inertial Navigation Systems
(Nauka, Moscow, 1992)
[in Russian]. |
| 13. | L. A. Fokin and A. G. Shchipitsyn,
"Strapdown Inertial Navigation Systems for High Precision Near-Earth Navigation
and Satellite Geodesy: Analysis of Operation and Errors,"
Izv. Akad. Nauk. Teor. Sist. Upr.,
No. 3, 164-176 (2008)
[J. Comput. Syst. Sci. Int. (Engl. Transl.)
47 (3), 485-497 (2008)]. |
| 14. | V. P. Seleznev and N. V. Selezneva,
Navigational Bionics
(Mashinostroenie, Moscow, 1987)
[in Russian]. |
| 15. | "Information about the Meeting of the Scientific Council in `General Mechanics',"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 2, 204-205 (1970)
[Mech. Solids. (Engl. Transl.)]. |
| 16. | Mechanics and Navigation.
Proc. of Scientific Session
Dedicated to A. Yu. Ishlinskii on the Occasion of His 85th Birthday (Inst. for Problems in Mechanics, RAS, Moscow, September 30, 1998)
(GHTs RF-TsNII "Elektropribor," St. Petersburg, 1999)
[in Russian]. |
| 17. | V. N. Branets, E. A. Mikrin, V. N. Platonov, et al.,
"Navigation Support of International Space Station,"
in Xth St.Petersburg Intern. Conf. in Integral Navigation Systems
(GHTs RF-TsNII "Elektropribor," St. Petersburg, 2003),
pp. 7-13
[in Russian]. |
| 18. | V. Ph. Zhuravlev,
"On the Solution of Equations of the Linear Oscillator with Respect to the Matrix
of the Inertial Trihedron,"
Dokl. Ross. Akad. Nauk
404 (4), 491-495 (2005)
[Dokl. Phys. (Engl. Transl.)
50 (10), 519-523 (2005)]. |
| 19. | V. Ph. Zhuravlev,
"A Strapdown Inertial System of Minimum Dimension
(A 3D Oscillator as a Complete Inertial Sensor),"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 5-10 (2005)
[Mech. Solids (Engl. Transl.)
40 (5), 1-5 (2005)]. |
| 20. | K. Popper,
"What is the Dialectics,"
Voprosy Filosofii,
No. 1, 118-138 (1995). |
| 21. | G. B. Malykin and G. V. Permitin,
"Thomas Precession,"
in Physical Encyclopedia, Vol. 5
(Bol'shaya Ros. Entsiklopediya, Moscow, 1998),
p. 123
[in Russian]. |
| 22. | L. Belloni and C. Reina,
"Thomas Precession; Sommerfeld Approach,"
in Einstein Collection, 1984-1985
(Nauka, Moscow, 1988),
pp. 201-214
[in Russian]. |
| 23. | Yu. M. Shirokov,
"Lorentz Transformations,"
in Physical Encyclopedic Dictionary, Vol. 3
(Sov. Entsiklopediya, Moscow, 1963),
pp. 17-19
[in Russian]. |
| 24. | D. D. Sokolov,
"Lorentz Transformation,"
in Mathematical Encyclopedia, Vol. 3
(Sov. Entsiklopediya, Moscow, 1982),
pp. 453-454
[in Russian]. |
| 25. | M. I. Voitsekhovskii,
"Boost,"
in Mathematical Physics. Encyclopedia
(Bol'shaya Ros. Entsiklopediya, Moscow, 1998),
p. 63
[in Russian]. |
| 26. | L. P. Grishchuk,
"Lorentz Transformations,"
in Physical Encyclopedia, Vol. 2
(Sov. Entsiklopediya, Moscow, 1990),
pp. 608-609
[in Russian]. |
| 27. | H. Poincaré,
"On the Dynamics of the Electron,"
in Relativity Principle,
Collection of Papers in Special Theory of Relativity
(Atomizdat, Moscow, 1973),
pp. 118-161
[in Russian]. |
| 28. | M.-A. Tonnelat,
The Principles of Electromagnetic Theory and of Relativity
(Masson, Paris, 1959; Izd-vo Inostr. Lit., Moscow, 1962; Springer, 1966). |
| 29. | C. Møller,
The Theory of Relativity
(Clarendon Press, Oxford, 1952; Atomizdat, Moscow, 1975). |
| 30. | Ch. W. Misner, K. S. Thorne, and J. A. Wheeler,
Gravitation, Vol. 3
(Freeman, 1973; Mir, Moscow, 1977). |
| 31. | A. A. Logunov,
Henri Poincaré and Relativity Theory
(Nauka, Moscow, 2004)
[in Russian]. |
| 32. | I. Kobzarev,
"Introduction,"
in Einstein Collection, 1984-1985
(Nauka, Moscow, 1988),
pp. 5-6
[in Russian]. |
| 33. | G. B. Malykin,
"Thomas Precession: Correct and Incorrect Solutions,"
Uspekhi Fiz. Nauk
176 (8), 865-882 (2006)
[Phys. Uspekhi (Engl. Transl.)
49 (8), 837-855 (2006)]. |
| 34. | I. Yu. Kobzarev,
"Theory of Relativity,"
in Physical Encyclopedia, Vol. 3
(Bol'shaya Ros. Entsiklopediya, Moscow, 1992),
pp. 493-502
[in Russian]. |
| 35. | K. Caratheodory,
"To the Axiomatics of the Special Theory of Relativity,"
in Progress in Contemporary Physics
(Nauka, Moscow, 1964),
pp. 167-187
[in Russian]. |
| 36. | M. I. Monastyrskii,
"Quaternions,"
in Physical Encyclopedia, Vol. 2
(Sov. Entsiklopediya, Moscow, 1990),
p. 345
[in Russian]. |
| 37. | N. V. Aleksandrova,
History of Mathematical Terms, Concepts, Notation,
Dictionary-Reference Book
(Izd-vo LKI, Moscow, 2007)
[in Russian]. |
| 38. | L. S. Polak,
William Hamilton: 1805-1865
(Nauka, Moscow, 1993)
[in Russian]. |
| 39. | V. F. Chub,
"On the Possibility of Application of one System of Hypercomplex Numbers in Inertial Navigation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 3-23 (2002)
[Mech. Solids (Engl. Transl.)
37 (6), 1-17 (2002)]. |
| 40. | 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]. |
| 41. | Yu. N. Chelnokov,
Quaternion Models and Methods of Dynamics, Navigation, and Motion Control
(Fizmatlit, Moscow, 2011)
[in Russian]. |
| 42. | V. V. Malanin and N. A. Strelkova, Optimal Control of Attitude and Helical Motion of a Rigid Body (NITs "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2004) [in Russian]. |
| 43. | D. E. Burlankov,
Time, Space, Gravity
(NITs "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2006)
[in Russian]. |
| 44. | A. Lightman, W. Press, R. Price, and S. Teukolsky,
Problem Book in Relativity and Gravitation
(Princeton Univ. Press, Princeton, 1975; Mir, Moscow, 1979). |
| 45. | A. P. Efremov,
Quaternion Spaces, Reference Systems, and Fields
(Izd-vo RUDN, Moscow, 2005)
[in Russian]. |
| 46. | E. V. Zakharova,
"New Books on Physics and Related Sciences,"
Uspekhi Fiz. Nauk
173 (10), 1149-1152 (2003)
[Phys. Uspekhi (Engl. Transl.)
46 (10), 1117-1120 (2003)]. |
| 47. | V. F. Chub,
"Use of the Conformal Group in the Theory of Inertial Navigation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 3-17 (2006)
[Mech. Solids (Engl. Transl.)
41 (5), 1-12 (2006)]. |
| 48. | R. H. Cannon Jr.,
"Requirements and Design for a Special Gyro for Measuring General Relativity Effects
from an Astronomic Satellite,"
in Problems of Gyroscopy
(Mir, Moscow, 1967),
pp. 129-143
[in Russian]. |
| 49. | V. B. Braginskii,
"Gravitational Experiments from Cavendish to the Present,"
Priroda,
No. 12, 70-75 (1981). |
| 50. | I. Lisov,
"Was Einstein so Right
The Gravity Probe-B Was Placed into Orbit 45 Years Later after the Birth of the Idea?"
Novosti Kosmonavt.
14 (6), 30-33 (2004). |
| 51. | I. Lisov,
"The Gravity Probe-B is in Operation,"
Novosti Kosmonavt.
14 (11), 48-49 (2004). |
| 52. | V. G. Peshekhonov,
"A Unique Gyro Ensured Verification of General Relativity,"
Giroskop. Navigats.,
No. 4, 111-114 (2007). |
| 53. | V. Ph. Zhuravlev,
"Limiting Accuracy of an Ideal Gyroscope,"
Dokl. Ross. Akad. Nauk
410 (2), 200-202 (2006)
[Dokl. Phys. (Engl. Transl.)
51 (9), 517-519 (2006)]. |
| 54. | V. Ph. Zhuravlev,
"On the Limiting Accuracy of a Free Gyro,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 5-9 (2006)
[Mech. Solids (Engl. Transl.)
41 (4), 1-4 (2006)]. |
| 55. | A. V. Berkov, E. D. Zhizhin, and I. Yu. Kobzarev,
Einstein's Gravitation Theory and Its Experimental Consequencies
(Izd-vo MIFI, Moscow, 1981)
[in Russian]. |
| 56. | A. A. Logunov,
Theory of Gravitational Field
(Nauka, Moscow, 2000)
[in Russian]. |
| 57. | D. E. Burlankov and G. B. Malykin,
"Thomas Precession by Pseudoquaternions,"
Giperkompl. Chisla Geom. Fiz.
2 (2(4)), 147-152 (2005). |
| 58. | V. A. Bordovitsyn and V. V. Telushkin,
"Thomas Precession and Spin,"
Izv. Vyssh. Uchebn. Zaved. Fiz.
49 (11), 81-86 (2006)
[Russ. Phys. J. (Engl. Transl.)
49 (11), 1241-1248 (2006)]. |
| 59. | V. I. Ritus,
"On the Difference between Wigner's and Møller's Approaches to the Description of Thomas Precession,"
Uspekhi Fiz. Nauk
177 (1), 105-112 (2007)
[Phys. Uspekhi (Engl. Transl.)
177 (1), 95-102 (2007)]. |
| 60. | E. A. Nemchenko, "On Thomas precession in the Classical Theory of Relativistic Radiation," Izv. Vyssh. Uchebn. Zaved. Fiz.
54 (3), 86-88 (2011) [Russ. Phys. J. (Engl. Transl.)
54 (3), 360-363 (2011)]. |
| 61. | J. D. Jackson,
Classical Electrodynamics
(Wiley, 1962; Mir, Moscow, 1965)
[in Russian]. |
| 62. | G. B. Malykin,
"The Relation of Thomas Precession to Ishlinskii's Theorem
as Applied to the Rotating Image of a Relativistically Moving Body,"
Uspekhi Fiz. Nauk
169 (5), 585-590 (1999)
[Phys. Uspekhi (Engl. Transl.)
169 (5), 505-509 (1999)]. |
| 63. | G. B. Malykin,
"The Application of the Solid-Angle Theorem in the Special Theory of Relativity,"
Prikl. Mat. Mekh.
63 (5), 775-780 (1999)
[J. Appl. Math. Mech. (Engl. Transl.)
63 (5), 731-735 (1999)]. |
| 64. | G. A. Zaitsev,
"On the Relation between the Theory of Relativity and the Theory of Groups,"
in M.-A. Tonnelat,
The Principles of Electromagnetic Theory and of Relativity
(Izd-vo Inostr. Lit., Moscow, 1962),
pp. 447-475
[in Russian]. |
| 65. | A. V. Babichenko and A. P. Rogalev,
"To the Problem of the SINS Algorithm Accuracy Control,"
Aviakosmich. Priborostr.,
No. 10, 27-29 (2006). |
| 66. | V. F. Chub,
"On the Uniformly Accelerated Motion,"
Fizich. Obrazov. VUZ
11 (3), 127-130 (2005). |
| 67. | V. F. Chub,
"Nonclosure of Elemenary Space-Time Transformations,"
Giperkompl. Chisla Geom. Fiz.
2 (2(4)), 153-160 (2005). |
| 68. | V. F. Chub,
"Inertial Navigation Equations and the Quaternion Space-Time Theory,"
Giperkompl. Chisla Geom. Fiz.
4 (1(7)), 133-140 (2007). |
| 69. | V. F. Chub,
"Formulation of the Problem of Inertial Navigation: A Group Theory Approach,"
Kosmich. Issled.
45 (2), 189-192 (2007)
[Cosmic. Res. (Engl. Transl.)
45 (2), 176-179 (2007)]. |
| 70. | V. F. Chub,
"Statement of the Two-Body Problem in the Parameters of the Extended Galilei Group,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 16-20 (2012)
[Mech. Solids (Engl. Transl.)
47 (4), 385-389 (2012)]. |
| 71. | V. F. Chub,
"Inertial Navigation Teaching Methods for Students of Physical-Technical Institute,"
Fizich. Obrazov. VUZ
18 (3), 137-145 (2012). |
|
| Received |
29 June 2011 |
| Link to Fulltext |
|
| << Previous article | Volume 49, Issue 2 / 2014 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English