Abstract
The purpose of this chapter is to present part of basic properties of vector and tensor operations, which is frequently used in the rest of the book. At first, the laws of vector addition, scalar multiplication, scalar product, vector product and triple products, etc. are presented. Next, the definitions and attributes of dual vector are introduced in the same manner. Then, the tensor definition and its calculation are discussed. The second order tensor is selected as a special case to express the tensor manipulations in detail. Many types of tensors are involved, such as rotation tensor, curvature tensor, and the metric tensor for surface and three-dimensional mapping. Finally, the motion tensor is introduced with the aid of geometric description of infinitesimal motion for a line vector.
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Wang, J. (2023). Vector and Tensor. In: Multiscale Multibody Dynamics. Springer, Singapore. https://doi.org/10.1007/978-981-19-8441-9_1
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DOI: https://doi.org/10.1007/978-981-19-8441-9_1
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