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Tensor Calculus and Analytical Dynamics (Library of Engineering Mathematics) [Englisch] [Gebundene Ausgabe]

John G. Papastavridis , J. G. Papastavridis

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Kurzbeschreibung

Dezember 1998 Library of Engineering Mathematics (Buch 4)
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

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"This is a deep and complete workin view of the fact that very few books in tensor analysis have appeared recently, the present monograph is one of the most up to datehighly recommended" -L.Y. Bahar in Applied Mechanics Review, September 1999 "The book is very carefully written and published, it should find many readers and young scientists who want to follow the beautiful Analytical Dynamics in research and teaching." -Professor Peter MaiBer Applied Mechanics Review, September 1999 "The material covered in the book is certainly of a high interest in spite of the long tradition accumulated in the past and a considerable number of textbooks published... the book is intended to be a concise introductory tool to theoretical dynamics and aims to provide the reader with a strong background on the geometrical concepts supporting the formulation of the general equations of motion of constrained mechanical systems... Papastavridis achieves his purpose in handing down a coherent and understandable presentation inclusive of some solved examples and problems... The volume represents a valuable contribution to the dissemination of knowledge in the field of theoretical mechanics and may be recommended for graduate students and researchers in engineering, physics, and applied mathematics." -Meccanica, vol. 35, #5, 2001

Synopsis

"Tensor Calculus and Analytical Dynamics" provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, "Tensor Calculus and Analytical Dynamics" contains uniquely accessible treatments of such intricate topics as: tensor calculus in nonholonomic variables and Pfaffian nonholonomic constraints related integrability theory of Frobenius. The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

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Einleitungssatz
Tensor calculus (TC) is a branch of geometry that allows us to formulate geometrical and physical theorems (usually as differential equations) in terms of general, i.e., curvilinear, coordinates and components of the pertinent quantities, that are independent, or form invariant, of the particular system of coordinates used for their descriptions -- hence its older name: absolute differential calculus. Lesen Sie die erste Seite
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Amazon.com: 4.8 von 5 Sternen  4 Rezensionen
19 von 19 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen The definitive book on tensors in analytical mechanics 28. August 2000
Von Hanno Essen - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
This book is not a text book. It is, in some sense, the final word on tensor formalism in finite degree of freedom (analytical) mechanics. It is one of the most scholarly books I have come across. The list of references is very exhaustive and the author is well read in the literature on the subject, not just in english, but also in russian, french, and german. The style is clear and concise, the notation is carefully chosen and summarized in a useful section where conventions, notation, and basic formulae are listed.
7 von 7 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen comprehensive but biased view of tensor analysis... 25. Januar 2006
Von O. Burak Okan - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
Papastavridis is an author with a unique attitude towards mathematics. He avoids the coordinate free formulation of tensors on manifolds. In his view, the exterior differential calculus is an esoteric abstraction which is hard to grasp by many and thus has the danger of turning down able people from embarking on doing research in analytical mechanics. This is basically a recapitulation of his views which have been explicitly stated within the book in a broader context.

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.
2 von 2 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen The best reference on the tensorial foundation of analytical mechanics 28. Januar 2011
Von Joshua Ashenberg - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
This is probably the best book in the English language on the tensorial foundation of analytical mechanics. The book presents rigorous derivations of the main concepts of mechanics, in particular integrability and the principles behind various approaches to the derivation of the equations of motion. Beside its analytical merit, the book is a service to the English reader since the best references so far on non-holonomic systems are in German, Russian and French. In addition there are several notations in the classical literature on tensors, i.e., those of Eisenhart, Levi-Civita, Schouten and Synge, with different books use different notations; this book unifies them all.
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. And then a major part is dedicated to different approaches for the derivation of the equations of motion, under constraints, based on Lagrange's principle. There is a comprehensive discussion of constraints, in particular non-holonomic Pfaffians including geometrical considerations/illustrations. The book ends with helpful examples that demonstrate the various methods and the non-integrability concept. There are many more important features in this book, but I'm trying to keep this review short.
Be aware that this book aims for the mathematician and for the analytical minded physicist and engineer. It is demanding reading and requires a solid mathematical background. For the right reader it is a great read and an excellent reference. I tried to give it six stars, but Amazon's limit is five ... .
5.0 von 5 Sternen An excellent book and a must-read for anybody who works in research of a branch of Mechanics 15. August 2011
Von Alexandru Stere - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Verifizierter Kauf
I have purchased Professor Papastavridis' book while waiting for his other masterpiece, the Analytical Mechanics treatise. I congratulate myself for this wise decision. Don't let yourself fooled by the apparent abundant set of formulae. That is because Professor Papastavridis is a rigorous person who doesn't allow room for double guessing. For the pen and paper reader, this will be a wonderful journey. The text between formulae is loaded with clear explanations and the references send the reader who has time on his hands to other excellent books. I read about quasi-coordinates in so many other books, but for the first time Professor Papastavridis made me understand the concept. And when I say "understand", is not only the "ok, and what?", as it is rather the "aha! that means...". This book is a superb piece of scientific work by a great scholar. Worth every cent!!!
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