Elementary Vector Analysis (Classic Reprint): With Application to Geometry and Physics - Couverture souple

C. E. Weatherburn

Couverture souple

ISBN 10 : 1330407520 ISBN 13 : 9781330407523

Editeur : Forgotten Books, 2018

Synopsis

Master the fundamentals of vector analysis with clear, practical guidance.

This book introduces the key ideas of how vectors behave in motion and how to apply them to geometry and physics. It covers changing frames of reference, relative motion, and the math needed to describe rotations, derivatives, and integrals in a rigorous but accessible way.

You’ll find concrete developments of topics such as Coriolis’ theorem, Euler’s equations for rigid bodies, and curvature and torsion of curves. The text connects these ideas to problems in mechanics and engineering, offering a solid foundation for both theory and application.

• How to relate velocities and accelerations seen from different frames of reference


• Derivation and use of Coriolis’ theorem in dynamics


• Euler’s dynamical equations and their applications to rigid bodies


• Concepts of curvature, torsion, and the geometry of curves

Ideal for readers of physics and engineering who want a rigorous, readable treatment of vector methods and their applications.

A propos du livre

Présentation de l'éditeur

My object in writing this book was to provide a simple exposition of elementary Vector A nalysis, and to show how it may be employed with advantage in Geometry and Mechanics. It was thought unnecessary, in the present volume, to enter upon the more advanced parts of the subject, built upon the ideas of gradient, curl and divergence. Vector algebra and the differentiation of vectors with respect to one scalar variable furnish a powerful instrument even for the higher parts of dynamics. The work does not claim to be a complete text-book in either Geometry or Mechanics, though a good deal of ground is covered in both subjects. The use of vector analysis in the former is abundantly illustrated by the treatment of the straight hne, the plane, the sphere and the twisted curve, which are dealt with as fully as in most elementary books, and a good deal more concisely. In Mechanics I have explained and proved all the important elementary principles. The equations of equilibrium for a rigid body are deduced from the equations of motion. This is contrary to the ordinary practice and, of course, is not recommended for young beginners. But for a student who is able to read this volume, it is certainly desirable to show that the principles of statics are only particular cases of the dynamical ones, and that the long line of argument followed by text-books in Statics, to prove the theorems about moments, parallel forces, couples and the equilibrium of bodies, is really unnecessary. All these theorems are immediately deducible from the equations of motion of a rigid body, as shown in Chapter VIII. A nother departure from the ordinary practice has been made in connection with the theory of centroids.
(Typographical errors above are due to OCR software and don't occur in the book.)

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Présentation de l'éditeur

Excerpt from Elementary Vector Analysis With Application to Geometry and Physics

My object in writing this book was to provide a simple exposition of elementary Vector Analysis, and to show how it may be employed with advantage in Geometry and Mechanics. It was thought unnecessary, in the present volume, to enter upon the more advanced parts of the subject, built upon the ideas of gradient, curl and divergence. Vector algebra and the differentiation of vectors with respect to one scalar variable furnish a powerful instrument even for the higher parts of dynamics.

The work does not claim to be a complete text-book in either Geometry or Mechanics, though a good deal of ground is covered in both subjects. The use of vector analysis in the former is abundantly illustrated by the treatment of the straight line, the plane, the sphere and the twisted curve, which are dealt with as fully as in most elementary books, and a good deal more concisely. In Mechanics I have explained and proved all the important elementary principles. The equations of equilibrium for a rigid body are deduced from the equations of motion. This is contrary to the ordinary practice and, of course, is not recommended for young beginners. But for a student who is able to read this volume, it is certainly desirable to show that the principles of statics are only particular cases of the dynamical ones, and that the long line of argument followed by text-books in Statics, to prove the theorems about moments, parallel forces, couples and the equilibrium of bodies, is really unnecessary. All these theorems are immediately deducible from the equations of motion of a rigid body, as shown in Chapter VIII.

Another departure from the ordinary practice has been made in connection with the theory of centroids.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1330407520
• ISBN 13: 9781330407523
• Reliure: Broché
• Nombre de pages: 214
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