Abstract

The paper deals with the one-parameter family of Gordon–Schowalter objective derivatives including the Oldroyd, Cotter–Rivlin, and Jaumann derivatives. For a simple shear, movable bases are found in which the considered differential operators are reduced to the total time derivatives of the tensor components. For all derivatives of the family under consideration, except for Oldroyd and Cotter–Rivlin derivatives, the basis vectors lying in the shear plane rotate with a certain period changing their length and mutual orientation.

中文翻译：

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简单剪切下戈登-舒瓦尔特客观衍生物家族的拉格朗日表示

摘要

本文涉及戈登-肖瓦尔特目标导数的一参数族，包括Oldroyd，Cotter-Rivlin和Jaumann导数。对于简单的剪切，找到了可移动的基础，其中考虑的微分算子被简化为张量分量的总时间导数。对于考虑中的该族的所有导数，除了Oldroyd和Cotter–Rivlin导数之外，剪切平面中的基向量会旋转一定的时间，从而改变其长度和相互朝向。