Frame-indifference of cross products,rotations,and the permutation tensor  

作　　者：Maolin Du 

机构地区：[1]Department of Civil Engineering,Sanjiang University,Nanjing 210012,China

出　　处：《Theoretical & Applied Mechanics Letters》2020年第2期116-119,共4页力学快报（英文版）

基　　金：National Natural Science Foundation of China(No.51978166);the Research Fund of Sanjiang University(No.2018SJKY005)。

摘　　要：Under improper transformations,the traditional transformation laws for cross products,the permutation tensor,and rotations are incorrect.For a cross product,using a counter-example the left-hand rule is proved wrong.The unique rule for a cross product is the right-hand rule.Coordinate systems have handedness,while a cross product is frame-indifference.Since the permutation tensor is defined as a triple product including a cross product,the law for the permutation tensor is false.For a rotation,its pseudovector representation is incorrect,because the mirror is an auxiliary device to produce the virtual image rather than a new coordinate system or reference frame.

关 键 词：Pseudovector Cross product IMPROPER transformation Handed coefficient PERMUTATION TENSOR 

分 类 号：O183.2[理学—数学]