Applying Calculations of Quaternionic Matrices for Formation of the Tables of Directional Cosines

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Kravets, Victor; Kravets, Tamila; Burov, Olexiy

Applying Calculations of Quaternionic Matrices for Formation of the Tables of Directional Cosines Journal Article

Mechanics, Materials Science & Engineering, 11 , 2017, ISSN: 2412-5954.

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Authors: Victor Kravets, Tamila Kravets, Olexiy Burov

ABSTRACT. The mathematical apparatus of monomial (1,0,-1)-matrices-(4×4) is applied to the description of the turn in space in the moving (bound) and fixed (inertial) frames of reference. A general algorithm for the formation of transformation matrices of the sequence of three independent turns with repetition and in opposite directions is proposed. A finite set of systems of three independent turns is constructed, consisting of 96 variants and including known systems of angles. The algorithm is approved for the formation of tables of directing cosines of the Euler-Krylov angles systems, aircraft angles, Euler angles, nautical angles. The proposed algorithm for generating directional cosine tables meets both the aesthetic criteria, expressed in orderliness, laconism, convenience of analytical transformations, and the utilitarian needs of computer technologies, providing a mathematically elegant, compact, universal matrix algorithm that, on whole, increases the productivity of intellectual labor.

Keywords: monomial (1,0,-1)-matrices-(4×4), quaternionic matrices, parameters of Rodrigues-Hamilton, finite turn, matrices of directional cosines

DOI 10.2412/mmse.78.59.591

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