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Sixth-order Isotropic Descartes Tensor

Author: YinHongRan
Tutor: WuWei
School: Tianjin University
Course: Applied Mathematics
Keywords: Tensor Invariant Isotropic tensor Symmetry tensor
CLC: R445.2
Type: Master's thesis
Year: 2010
Downloads: 15
Quote: 0
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Abstract


Tensor analysis is an important tool in theoretical physics,continuum mechanics and many other areas of science and engineering.This paper is concerned with the isotropic tensor. It is a special kind of tensor. In this paper, we main study on its expression.This article first introduces the diagonal line coordinates in the three-dimensional coordinate system、the transformation between vector-based、the definition of ten-sor、the concept of isotropic and four special transformation.On this basis,we draw the general representation of the second、third and fourth-order isotropic symmetry descartes tensor.Then we extend the fifth-order isotropic descartes tensor to the six-order isotropic descartes tensor and obtain the general representation of sixth-order isotropic descartes tensor.The general representation of sixth-order isotropic descartes tensor is:

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