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Mathematics of random phenomena: Random vibrations of mechanical structures

Mathematics of random phenomena: Random vibrations of mechanical structures BOOK REVIEWS 195 of the gravitational physics are the best parts of the book. The principle of equivalence is used in order to define a metric in the presence of a gravitational field via the local geodesic frames. It is interesting to point out that by using the same approach one can actually define metric connection on an arbitrary (pseudo-) Riemannian manifold (cf. R. D. Richtmyer, Principles of Advanced Mathematical Physics, vol. 2, Springer-Verlag, 1981). Further, the book contains neat reports on Schwartzehild metric, gravitational waves, cosmological models, and other related topics. The opening chapters are devoted to an accurate treatment of the special theory including Maxwell's equations and the energy- momentum tensor. Goodbody's book is an interesting mixture of three-dimensional linear algebra and theoretical mechanics. It fills a psychological gap between the 'abstract' linear algebra and dynamics via the systematic use of tensor products (of vectors). How many (under)graduates know that the tensor products of vector spaces have something to do with, say, inertia tensor? The author shows convincingly that the simple formula (a(~b).c= a(b, c) (a definition of the decomposable second-order Cartesian tensor!) can be successfully used for concrete calculations in mechanics, fluid mechanics, and elasticity theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Mathematics of random phenomena: Random vibrations of mechanical structures

Acta Applicandae Mathematicae , Volume 11 (2) – May 3, 2004

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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00047290
Publisher site
See Article on Publisher Site

Abstract

BOOK REVIEWS 195 of the gravitational physics are the best parts of the book. The principle of equivalence is used in order to define a metric in the presence of a gravitational field via the local geodesic frames. It is interesting to point out that by using the same approach one can actually define metric connection on an arbitrary (pseudo-) Riemannian manifold (cf. R. D. Richtmyer, Principles of Advanced Mathematical Physics, vol. 2, Springer-Verlag, 1981). Further, the book contains neat reports on Schwartzehild metric, gravitational waves, cosmological models, and other related topics. The opening chapters are devoted to an accurate treatment of the special theory including Maxwell's equations and the energy- momentum tensor. Goodbody's book is an interesting mixture of three-dimensional linear algebra and theoretical mechanics. It fills a psychological gap between the 'abstract' linear algebra and dynamics via the systematic use of tensor products (of vectors). How many (under)graduates know that the tensor products of vector spaces have something to do with, say, inertia tensor? The author shows convincingly that the simple formula (a(~b).c= a(b, c) (a definition of the decomposable second-order Cartesian tensor!) can be successfully used for concrete calculations in mechanics, fluid mechanics, and elasticity theory.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 3, 2004

There are no references for this article.