Mathematical Aspects of Classical and Celestial Mechanics

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 explore...

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Main Authors: Arnold, Vladimir I., Kozlov, Valery V. (Author), Neishtadt, Anatoly I. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2006, 2006
Edition:3rd ed. 2006
Series:Encyclopaedia of Mathematical Sciences
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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505 0 |a 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 
653 |a Dynamical Systems and Ergodic Theory 
653 |a Ergodic theory 
653 |a Partial Differential Equations 
653 |a Mathematical physics 
653 |a Partial differential equations 
653 |a Theoretical, Mathematical and Computational Physics 
653 |a Ordinary Differential Equations 
653 |a Differential equations 
653 |a Dynamics 
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700 1 |a Neishtadt, Anatoly I.  |e [author] 
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520 |a 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