论文标题
关于矢量场梯度的Gibbsian表示的注释
A Note on the Gibbsian Representation of the Gradient of a Vector Field
论文作者
论文摘要
在本说明中，我们提供了一个熟悉的主题的重要考虑因素：向量字段的梯度。矢量场的梯度是连续力学中表示的常见数量。但是，即使对于笛卡尔坐标系，该数量的共同用途也有两种不同的表示，这导致了某些结果的歧义。我们回顾了导致\ emph {gibbsian表示}的历史记录，并提供了一些建议，以帮助阐明常规吉布斯矢量或张量表示时阐明此术语的含义。在附录中，我们简要扩展了与几何代数（GA）框架中变形和旋转张量的Gibbsian表示的联系。
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems, there are two different representations for this quantity in common use, which leads to ambiguity in some results. We review the history leading to the \emph{Gibbsian representation} for the gradient of a vector field, and provide some suggestions to help clarify the meaning of such terms when represented in conventional Gibbsian vector or tensor notation. In an appendix, we briefly expand on the connection with the Gibbsian representation of the deformation and rotation tensors in the framework of geometric algebra (GA).
