The criterion for transferable self-consistently translationality of coordinate transform operators and reference frames in universal kinematics

Grushka Yaroslav

doi:https://doi.org/10.31861/bmj2021.01.10

Grushka Yaroslav ¹

¹ Department of nonlinear analysis, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, 01001, Ukraine

DOI: https://doi.org/10.31861/bmj2021.01.10

Keywords: universal kinematics, changeable sets, reference frames, linear coordinate spaces, coordinate transform operators, transferable self-consistently translationality

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Abstract

From an intuitive point of view universal kinematics are collections (sets) of changing objects, which evolve, being in a certain spatial-geometric environment, and evolution of which can be observed from many different frames of reference. Moreover, the definition of universal kinematics impose the existence of some (preassigned) universal coordinate transform between every two reference frames of such kinematics. Transferable self-consistently translational reference frames (in vector universal kinematics) are interesting because for such reference frames it is possible to give a clear and unambiguous definition of displacement of a moving reference frame relative to a fixed one, which does not depend on the choice of a fixed point in the moving frame of reference. In the present paper it is shown that an arbitrary reference frame $m$ is transferable self-consistently translational relatively to a reference frame $l$ (in some vector universal kinematics ${\mathcal F}$ ) if and only if the coordinate transform operator from the reference frame $m$ to the reference frame $l$ is transferable self-consistently translational. Therefore transferable self-consistently translational coordinate transform operators describe the conversion of coordinates from the moving and transferable self-consistently translational frame of reference to the (given) fixed frame in vector universal kinematics. Also in the paper it is described the structure of transferable self-consistently translational coordinate transform operators (this is the main result of the article). Using this result it have been obtained the necessary and sufficient condition for transferable self-consistently translationality of one reference frame relatively to another in vector universal kinematics.

References

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ACS Style: Grushka, Y. The criterion for transferable self-consistently translationality of coordinate transform operators and reference frames in universal kinematics. Bukovinian Mathematical Journal. 2021, 9 https://doi.org/https://doi.org/10.31861/bmj2021.01.10
AMA Style: Grushka Y. The criterion for transferable self-consistently translationality of coordinate transform operators and reference frames in universal kinematics. Bukovinian Mathematical Journal. 2021; 9(1). https://doi.org/https://doi.org/10.31861/bmj2021.01.10
Chicago/Turabian Style: Yaroslav Grushka. 2021. "The criterion for transferable self-consistently translationality of coordinate transform operators and reference frames in universal kinematics". Bukovinian Mathematical Journal. 9 no. 1. https://doi.org/https://doi.org/10.31861/bmj2021.01.10

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