 | | 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
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| In English (Mech. Solids): | | 4760 |
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| Yu.N. Chelnokov, "Orientation and Kinematics of Rotation: Quaternionic and Four-Dimensional Skew-Symmetric Operators, Equations, and Algorithms," Mech. Solids. 57 (8), 1885-1907 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
8 |
Pages |
1885-1907 |
| DOI |
10.3103/S0025654422080106 |
| Title |
Orientation and Kinematics of Rotation: Quaternionic and Four-Dimensional Skew-Symmetric Operators, Equations, and Algorithms |
| Author(s) |
Yu.N. Chelnokov (Institute for Precision Mechanics and Control Problems, Russian Academy of Sciences, Saratov, 410028 Russia, ChelnokovYuN@gmail.com) |
| Abstract |
This paper develops a theory of three- and four-dimensional skew-symmetric rotation
operators generated by exponential representations of orthogonal operators or their representations
using Cayley’s formulas. The generating orthogonal operators involve the direction angle cosine
matrix, the quaternionic matrix of Euler’s parameters, and the Hamilton rotation quaternion. Novel
matrix and quaternion kinematic equations for the rotation of a rigid body based on four-dimensional
skew-symmetric matrices and on quaternions with zero scalar parts (in associated quaternions) are
proposed. It is shown that they are advantageous compared to the known kinematic equations of rotation based on three-dimensional skew-symmetric matrices and vector kinematic equations. As a topical application of the proposed equations, the paper considers the construction of high-precision
algorithms for determining the orientation of a moving object in an inertial coordinate system using a
strapless inertial navigation system. Fourth-order (even-order) skew-symmetric matrices and associated quaternions have qualitative advantages over third-order (odd-order) skew-symmetric matrices
and vectors. This makes the use of the proposed kinematic equations of rotation in orientation and
navigation problems much more efficient compared to traditionally used equations in three-dimensional skew-symmetric operators. |
| Keywords |
three-dimensional and four-dimensional orthogonal and skew-symmetric rotation operators, matrices, vectors, quaternions, exponential representations of orthogonal operators, Cayley’s formulas, kinematic equations of rotation, orientation algorithms |
| Received |
30 May 2022 | Revised |
15 August 2022 | Accepted |
15 August 2022 |
| Link to Fulltext |
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