A derivation of the vector Lorentz transformation is given by explicitly compounding the pure Lorentz transformation along one spatial axis with pure spatial rotations. The orthogonal matrix is found which expresses the spatial rotation produced by two successive vector Lorentz transformations and is applied to the Thomas precession of an accelerated frame relative to an inertial one. The method used is basically that outlined in Møller's book.
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PAPERS| September 01 1967
Vector Lorentz Transformations
James T. Cushing; Vector Lorentz Transformations. Am. J. Phys. 1 September 1967; 35 (9): 858–862. https://doi.org/10.1119/1.1974267
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