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＜電子ブック＞
Mathematical Aspects of Classical and Celestial Mechanics / by Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt
(Encyclopaedia of Mathematical Sciences ; 3)

版	3rd ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XIII, 505 p : online resource
著者標目	*Arnold, Vladimir I author Kozlov, Valery V author Neishtadt, Anatoly I author SpringerLink (Online service)
件　名	LCSH:Dynamical systems LCSH:Mathematical physics LCSH:Differential equations FREE:Dynamical Systems FREE:Theoretical, Mathematical and Computational Physics FREE:Differential Equations
一般注記	Basic Principles of Classical Mechanics -- The n-Body Problem -- Symmetry Groups and Order Reduction -- Variational Principles and Methods -- Integrable Systems and Integration Methods -- Perturbation Theory for Integrable Systems -- Non-Integrable Systems -- Theory of Small Oscillations -- Tensor Invariants of Equations of Dynamics 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 HTTP:URL=https://doi.org/10.1007/978-3-540-48926-9

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