 | | 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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| V.F. Chub, "Statement of the Two-Body Problem in the Parameters of the Extended Galilei Group," Mech. Solids. 47 (4), 385-389 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
4 |
Pages |
385-389 |
| DOI |
10.3103/S0025654412040036 |
| Title |
Statement of the Two-Body Problem in the Parameters of the Extended Galilei Group |
| Author(s) |
V.F. Chub (Korolev Rocket and Space Corporation "Energia," Lenina 4A, Korolev, Moscow Oblast, 141070 Russia, v.chub@mail.ru) |
| Abstract |
The classical mechanical problem on the motion on a system of two or several bodies is stated in terms of parameters of the
13-parameter extended Galilean group (translations, rotations, boosts, and gravitational transformations) without using such traditional notions as "point" and "force." |
| Keywords |
n-body problem, group-theoretic approach, extended Galilei group |
| References |
| 1. | V. Ph. Zhuravlev,
Foundations of Theoretical Mechanics
(Fizmatlit, Moscow, 2008)
[in Russian]. |
| 2. | S. V. Gromov,
Physics: Mechanics. Relativity. Electrodynamics
(Prosveshchenie, Moscow, 2003)
[in Russian]. |
| 3. | M. B. Balk,
Elements of Space Flight Dynamic
(Nauka, Moscow, 1965)
[in Russian]. |
| 4. | I. M. Yaglom,
Geometric Transformations, Vol. 1: Motions and Similarity Transformations
(Gostekhizdat, Moscow, 1955)
[in Russian]. |
| 5. | V. N. Branets,
Lectures in the Theory of Strapdown Inertial Navigation Control Systems
(MFTI, Moscow, 2009)
[in Russian]. |
| 6. | S. N. Kirpichnikov and V. S. Novoselov,
Mathematical Aspects of Kinematics of Solids
(Izd-vo LGU, Leningrad, 1986)
[in Russian]. |
| 7. | V. P. Vizgin,
"Erlangen Program" and Physics
(Nauka, Moscow, 1975)
[in Russian]. |
| 8. | 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)]. |
| 9. | 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)]. |
| 10. | 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)]. |
| 11. | G. N. Duboshin,
Celestial Mechanics. Fundamental Problems and Methods
(Nauka, Moscow, 1968)
[in Russian]. |
| 12. | M. F. Subbotin,
Introduction to Theoretical Astronomy
(Nauka, Moscow, 1968)
[in Russian]. |
|
| Received |
22 June 2010 |
| Link to Fulltext |
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