Abstract
This chapter develops a system of mathematical concepts of great utility in all branches of physics. Linear operators and transformations are represented in terms of geometric algebra to facilitate computation. The group theory of rotations, reflections and translations is discussed in detail. The most important result is a compact spinor representation of finite rotations, which is shown to be a powerful computational device. This representation is used to develop the kinematics of rigid motions, which, in turn, is applied to the description of reference frames and motion with respect to moving frames.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Hestenes, D. (1987). Operators and Transformations. In: New Foundations for Classical Mechanics. Fundamental Theories of Physics, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4802-0_5
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DOI: https://doi.org/10.1007/978-94-009-4802-0_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-2526-4
Online ISBN: 978-94-009-4802-0
eBook Packages: Springer Book Archive