 | | 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 |
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| V.N. Branets, "Isomorphism of Mathematical Descriptions of the Rotation Operation," Mech. Solids. 53 (2), 234-239 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
2 |
Pages |
234-239 |
| DOI |
10.3103/S0025654418020152 |
| Title |
Isomorphism of Mathematical Descriptions of the Rotation Operation |
| Author(s) |
V.N. Branets (National Research Tomsk State University, pr. Lenina 36, Tomsk, 634050 Russia; JSC "Gazprom Space Systems", Russia, branets@gazprom-spacesystems.ru) |
| Abstract |
Currently the practice of constructing various algorithms of inertial navigation, including strapdown navigation system (SINS), indicates that two mathematical methods for describing rotation are mainly used: using quaternions or direction cosines. Moreover, in SINS algorithms it is often convenient to use two of these parameter systems in parallel: quaternions for the angular motion algorithms (the orientation problem), and the direction cosines for the problem of calculating speed and position. In this case, parallel calculation of these two groups of parameters is carried out under the assumption of an exact isomorphic accordance between them. However, if the formalism of quaternions is single-valued, then the apparatus of matrix operations using direction cosines does not possess such a feature and admits several interpretations, which should be borne in mind. From this point of view, the question posed in this article makes sense not only as the question of the existence of an isomorphic accordance (there is no doubt about it), but in what form it exists for the matrix formalism of direction cosines. |
| Keywords |
kinematic transformations, bases, vectors, quaternions, direction cosines |
| References |
| 1. | V. N. Branets and I. P. Shmyglevsky,
Introduction to the Theory of Strapdown Inertial Navigation Systems
(Nauka, Moscow, 1992)
[in Russian]. |
| 2. | A. P. Bezhko, V. N. Branets, Yu. M. Zakharov, and I. P. Shmyglevsky,
"Application of Quaternions in the Theory of Finite Rotation of a Solid,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 1, 123-134 (1971)
[Mech. Solids (Engl. Transl.)]. |
| 3. | V. N. Branets and I. P. Shmyglevsky,
Application of Quaternions in Problems of Attitude Control of a Rigid Body
(Nauka, Moscow, 1973)
[in Russian]. |
| 4. | V. Ph. Zhuravlev,
Foundations of Theoretical Mechanics
(Fizmatgiz, Moscow, 2001)
[in Russian]. |
| 5. | M. L. Lidov,
Lectures on Theoretical Mechanics
(Fizmatgiz, Moscow, 2010)
[in Russian]. |
| 6. | V. N. Branets,
Lectures on the Theory of Strapdown Inertial Navigation Systems
(MFTI, Moscow, 2009)
[in Russian]. |
|
| Received |
07 November 2016 |
| Link to Fulltext |
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