Abstract
Vectors are used to describe basic quantities in mechanics including displacement, velocity, acceleration, force, torque, and momentum. A matrix is a powerful tool for expressing relations among vectors described in different spaces. Quaternions, as an extension of the complex numbers, can be used to describe rotations and space transformations. Knowledge of vectors, matrices, and quaternions is also essential to understanding key concepts in mechanics such as mass properties of a rigid body (e.g., moment and product of inertia) and the laws governing a rigid body’s motion. This chapter will present the essential material on vectors and matrices to be used in the following chapters of the book.
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References
Johnson, L.W., Riess, R.D., Arnold, J.T.: Introduction to Linear Algebra. Addison Wesley, Reading, MA (2002)
Massey, W.S.: Cross products of vectors in higher dimensional Euclidean spaces. Am. Math. Mon. 90 (10), 697–701 (1983)
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Huang, L. (2017). Preliminaries on Vectors, Matrices, Complex Numbers and Quaternions. In: A Concise Introduction to Mechanics of Rigid Bodies. Springer, Cham. https://doi.org/10.1007/978-3-319-45041-4_1
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DOI: https://doi.org/10.1007/978-3-319-45041-4_1
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45040-7
Online ISBN: 978-3-319-45041-4
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