 | | 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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| Molodenkov A.V., Sapunkov Ya.G., Molodenkova T.V., and Perelyaev S.E., "Analytical Solutions in the Darboux Problem and the Bortz Equation and the Approach to Orientation Algorithms Based on Them," Mech. Solids. 55 (7), 1013-1020 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
7 |
Pages |
1013-1020 |
| DOI |
10.3103/S002565442007016X |
| Title |
Analytical Solutions in the Darboux Problem and the Bortz Equation and the Approach to Orientation Algorithms Based on Them |
| Author(s) |
Molodenkov A.V. (Institute of Precision Mechanics and Control, Russian Academy of Sciences, Saratov, 410028 Russia, molalexei@yandex.ru)
Sapunkov Ya.G. (Institute of Precision Mechanics and Control, Russian Academy of Sciences, Saratov, 410028 Russia, molalexei@yandex.ru)
Molodenkova T.V. (Gagarin Saratov State Technical University, Saratov, 410054 Russia, moltw@yandex.ru)
Perelyaev S.E. (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia, sergey-perelyaev@mail.ru) |
| Abstract |
We consider the problem of determining the angular position of a rigid body in space from
its known angular velocity and initial position (the Darboux problem) in the quaternion setting. Based
on the exact solution of the Bortz approximate differential equation with respect to the orientation
vector of the rigid body, we analytically solve the problem to determine the quaternion of the orientation of the rigid body for each arbitrary angular velocity and small rotation angle of the rigid body.
Based on this solution, we propose an approach to design a new algorithm to compute the orientation
of moving objects by means of strapdown inertial navigation systems. |
| Keywords |
analytical solution, orientation, arbitrary angular velocity, rigid body, strapdown INS, quaternion, algorithm |
| Received |
13 December 2018 | Revised |
10 May 2019 | Accepted |
06 June 2019 |
| Link to Fulltext |
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