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Tensor Calculus and Analytical Dynamics (Engineering Mathematics) 1st Edition
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Top Customer Reviews
With that said, don`t expect to find anything pertaining to modern differential geometric view of mechanics. However, this book presents one of the most extensive survey of tensor analysis with indices. The bibliography is indeed comprehensive, and a welcome feature in such a monograph.
Personally, I benefitted alot from this book both in terms of physical aspects of mechanics and in terms of classical tensor analysis. However, I still believe in the power of mathematical abstractions in grasping of the holistic image of a physical and/or mathematical entity. In this respect, the language of differential forms is rather important and allows further useful topological generalizations like cohomology. It is true that the current engineering/science curricula does not leave much space for the modern view, but this is ultimately where it will be heading to. Despite his dislike of exterior calculus, Papastavridis inevitably builds a strong basis for delving into tensor analysis on manifolds. For the latter Bishop and Goldberg is still the best choice with an unbeatable price.
The first part of the book presents the foundation of tensor calculus, Riemannian geometry and the general idea of integrability. These are stand alone chapters, no other references required. It is worth mentioning that the author avoids the more modern approaches of differential forms and exterior calculus; he does it all with tensors. The book then proceeds into kinematics and kinetics, formulated using strict tensorial properties, such as covariance, contravariance and absolute derivative, and using variational calculus - total displacement vs. virtual displacement, terminology used in deriving the transitivity equation/Hamel coefficients (those coefficients reflect integrability) and the important Frobenius integrability theorem (as opposed to recent approaches that use the concepts of involutive distributions and Lie algebra formulation, this book uses variational "deltas"). The book then presents a formulation of differential geometry on manifolds with application to a particle's motion on a surface.Read more ›