Abstract
While the laws of mechanics can be written in coordinate-free form, they can be solved, in most cases, only if expressed in component form. This requires that we introduce a basis. Though the standard Cartesian basis is often the simplest, the physics and geometry of a problem, and especially the so-called boundary conditions, may dictate another. For example, if we wished to study the temperature distribution in a body the shape of a parallelepiped, we would choose most likely a basis consisting of vectors lying along three co-terminal edges of the body. An aim of tensor analysis is to embrace arbitrary coordinate systems and their associated bases, yet to produce formulas for computing invariants, such as the dot product, that are as simple as the Cartesian forms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Simmonds, J.G. (1994). General Bases and Tensor Notation. In: A Brief on Tensor Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8522-4_2
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8522-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6424-8
Online ISBN: 978-1-4419-8522-4
eBook Packages: Springer Book Archive