Preprint Article Version 1 This version is not peer-reviewed

Operating on Tensors within Dynamic Coordinate Frames

Version 1 : Received: 18 June 2018 / Approved: 19 October 2018 / Online: 19 October 2018 (05:11:35 CEST)

How to cite: Afas, K.C. Operating on Tensors within Dynamic Coordinate Frames. Preprints 2018, 2018100433 (doi: 10.20944/preprints201810.0433.v1). Afas, K.C. Operating on Tensors within Dynamic Coordinate Frames. Preprints 2018, 2018100433 (doi: 10.20944/preprints201810.0433.v1).

Abstract

This paper puts forward an alteration for Tensor Calculus utliized in a coordinate system which is under a dynamic distortion drawing inspiration from similar fields such as the Calculus of Moving Surfaces (CMS). The paper establishes transformation laws for Tensors within these regions and establishes Operators such as the Tensorial Field Derivative which enforce a Tensorial Transformation on Tensors defined within a Dynamically Moving coordinate system. This variation of Tensor Calculus can be utilized to observe how disciplines such as QFT and Continuum Mechanics would change to accomodate for a distorting coordinate system and can be utliized to develop new theoretical models which account for this temporal distortion particularly within Biological Settings.

Subject Areas

dynamic; tensor; operator; moving coordinates; 4D space; invariant

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