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130626  eng 
020 


a 9783540489269

100 
1 

a Arnold, Vladimir I.

245 
0 
0 
a Mathematical Aspects of Classical and Celestial Mechanics
h Elektronische Ressource
c by Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt

246 
3 
1 
a Dynamical Systems III

250 


a 3rd ed. 2006

260 


a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 2006, 2006

300 


a XIII, 505 p
b online resource

505 
0 

a Basic Principles of Classical Mechanics  The nBody Problem  Symmetry Groups and Order Reduction  Variational Principles and Methods  Integrable Systems and Integration Methods  Perturbation Theory for Integrable Systems  NonIntegrable 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

700 
1 

a Kozlov, Valery V.
e [author]

700 
1 

a Neishtadt, Anatoly I.
e [author]

710 
2 

a SpringerLink (Online service)

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

490 
0 

a Encyclopaedia of Mathematical Sciences

856 


u https://doi.org/10.1007/9783540489269?nosfx=y
x Verlag
3 Volltext

082 
0 

a 515.48

082 
0 

a 515.39

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 nontrivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a nonempty boundary. Applications of the variational methods to the theory of stability of motion are indicated
