| Mathematical Aspects of Classical and Celestial Mechanics 2006 Edition Contributor(s): Arnold, Vladimir I. (Author), Khukhro, E. (Translator), Kozlov, Valery V. (Author) |
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ISBN: 3540282467 ISBN-13: 9783540282464 Publisher: Springer OUR PRICE: $237.49 Product Type: Hardcover - Other Formats Published: October 2006 Annotation: This work describes the fundamental principles, problems, and methods of classical mechanics. The main attention is devoted to the mathematical side of the subject. The authors have endeavored to give an exposition stressing the working apparatus of classical mechanics. The book is significantly expanded compared to the previous edition. The authors have added two chapters on the variational principles and methods of classical mechanics as well as on tensor invariants of equations of dynamics. Moreover, various other sections have been revised, added or expanded. The main purpose of the book is to acquaint the reader with classical mechanics as a whole, in both its classical and its contemporary aspects. The book addresses all mathematicians, physicists and engineers. From the reviews of the previous editions: .,." The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ..." American Mathematical Monthly, Nov. 1989. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Science | Physics - Mathematical & Computational - Mathematics | Differential Equations - General |
| Dewey: 531.015 |
| Series: Encyclopaedia of Mathematical Sciences |
| Physical Information: 1.32" H x 6.46" W x 9.32" (1.98 lbs) 505 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the "working" apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated. |