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Mechanics in Engineering ›› 2019, Vol. 41 ›› Issue (1): 1-9.doi: 10.6052/1000-0879-18-154

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A VIEWPOINT OF THE TENSORAL PROPERTY OF COORDINATE TRANSFORMATION COEFFICIENT AND ANALYSISON THE CONCEPT OF HYBRID TENSOR1)

YIN Yajun2)   

  1. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China
  • Received:2018-04-18 Online:2019-02-20 Published:2019-10-31

Abstract:

This paper discusses a basic problem: Is the coordinate transformation coefficient the component of a tensor? The conventional viewpoint is that the coordinate transformation coefficient is not the component of a tensor. To reveal the essence of the coordinate transformation coefficient, the basic concept of the tensor is revisited. A new concept, i.e. the hybrid tensor, is defined. On the basis of the new concept, the conventional viewpoint is negated: the coordinate transformation coefficient is indeed the component of a tensor. That is to say, it is the hybrid component of a metric tensor. Thus, the concept of tensors is extented.

Key words: coordinate transformation coefficient, hybrid tensor, hybrid component, the hybrid component of the metric tensor

CLC Number: 

  • O183