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Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Hamiltonian systems --- Hamiltonsystemen --- Invariance principles (Physics) --- Mathematical physics --- Mathematische fysica --- Physical mathematics --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Physique mathématique --- Physique théorique --- Symmetrie (Fysica) --- Symmetry (Chemistry) --- Symmetry (Physics) --- Symétrie (Physique) --- Systèmes hamiltoniens --- Topologie --- Topology --- Wiskundige fysica --- Hamiltonian systems. --- Mathematical physics. --- Symmetry (Physics). --- Topology.
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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.
Mechanics, Analytic. --- Celestial mechanics. --- Gravitational astronomy --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Analytical mechanics --- Kinetics --- Differentiable dynamical systems. --- Differential Equations. --- Differential equations, partial. --- Dynamical Systems and Ergodic Theory. --- Theoretical, Mathematical and Computational Physics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics. --- Ergodic theory. --- Mathematical physics. --- Differential equations. --- Partial differential equations. --- Physical mathematics --- Physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics
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From the reviews: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. 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 "This is a book to curl up with in front of a fire on a cold winter's evening. ..." SIAM Reviews, Sept. 1989.
Mechanics, Analytic. --- Celestial mechanics. --- Mécanique analytique --- Mécanique céleste --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical physics. --- Analysis. --- Theoretical, Mathematical and Computational Physics. --- 517.1 Mathematical analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Mathematics
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