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Matrices and engineering dynamics. (English) Zbl 0701.65017

Ellis Horwood Series in Engineering Science. Chichester: Ellis Horwood Limited; New York etc.: Halsted Press/a div. of Wiley. 541 p. £125.00/pbk (1987).
This textbook, for senior undergraduate students of mechanical and aeronautical engineering, deals essentially with engineering dynamics, but in addition, it contains a fully expanded prerequisite on matrices. It comprises two main parts which are mathematics of matrices (chapters 1, 2 and 3) and dynamics of mechanical systems (chapters 4, 5, 6, 7 and 8).
The first part not only displays all the matrix background which is required in an engineering course (up to the concept of functions of matrices); but in addition, it emphasizes the numerical methods for matrix inversion and for the determination of eigenvalues and eigenvectors.
In the second part, rather than to directly analyze different models of dynamical systems, the authors come back to the mechanical principles themselves (virtual work, Hamilton’s principle) so that we can get more insight in such problems as response and stability of linear systems (chapter 6), linear dynamics of distributed mechanical systems (chapter 7), dynamics of composite systems (chapter 8). The inclusion of this chapter is truly an original and interesting feature which is scarcely found in such textbooks. Many questions are considered in a detailed manner, like for instance the finite element technique, analysis of skeletal structures, Kron’s eigenvalue method.
Other special features include proof of Sylvester’s law of degeneracy, definition of matrix partial fractions, the inverse method for stability boundaries, and new proofs of Sylvester’s law of inertia and the Wittrick-Williams and Simpson counting algorithm.
Interesting characteristics: easy to read, clear printing, self- contained, pedagogically good, many illustrative basic examples. Less interesting: we would like to find some problems for solution at the end of each chapter, at least in the matrix part, where it would be easy to do it.
Reviewer: G.Jumarie

MSC:

65Fxx Numerical linear algebra
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
70-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems
15-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra
74Kxx Thin bodies, structures
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