General Bases and Tensor Notation

  • James G. Simmonds
Part of the Undergraduate Texts in Mathematics book series (UTM)

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.

Keywords

Triad Vigil 

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • James G. Simmonds
    • 1
  1. 1.Department of Applied MathematicsUniversity of VirginiaCharlottesvilleUSA

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