Tensor Calculus and Analytical Dynamics (Engineering Mathematics) [Hardcover]

John G. Papastavridis (Author)

Book Description

Publication Date: December 18, 1998 | ISBN-10: 0849385148 | ISBN-13: 978-0849385148 | Edition: 1

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.

Product Details

• Hardcover: 448 pages
• Publisher: CRC Press; 1 edition (December 18, 1998)
• Language: English
• ISBN-10: 0849385148
• ISBN-13: 978-0849385148
• Product Dimensions: 9.7 x 6.3 x 1.5 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 4.8 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #2,148,210 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

17 of 17 people found the following review helpful:

5.0 out of 5 stars The definitive book on tensors in analytical mechanics, August 27, 2000

By 

Hanno Essen (Stockholm Sweden) - See all my reviews
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This review is from: Tensor Calculus and Analytical Dynamics (Engineering Mathematics) (Hardcover)

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.

6 of 6 people found the following review helpful:

4.0 out of 5 stars comprehensive but biased view of tensor analysis..., January 25, 2006

By 

O. Burak Okan (Cambridge, MA USA) - See all my reviews
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This review is from: Tensor Calculus and Analytical Dynamics (Engineering Mathematics) (Hardcover)

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.

1 of 1 people found the following review helpful:

5.0 out of 5 stars The best reference on the tensorial foundation of analytical mechanics, January 28, 2011

By 

Joshua Ashenberg (Chelmsford, MA USA) - See all my reviews
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This review is from: Tensor Calculus and Analytical Dynamics (Engineering Mathematics) (Hardcover)

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 ... .