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AuthorArnold, V. I. author
TitleMathematical Aspects of Classical and Celestial Mechanics [electronic resource] / by V. I. Arnold, V. V. Kozlov, A. I. Neishtadt
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1997
Edition Second Edition
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Descript XIV, 294 p. online resource


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


1. Basic Principles of Classical Mechanics -- ยง 1. Newtonian Mechanics -- ยง 2. Lagrangian Mechanics -- ยง 3. Hamiltonian Mechanics -- ยง 4. Vakonomic Mechanics -- ยง 5. Hamiltonian Formalism with Constraints -- ยง 6. Realization of Constraints -- 2. The ?-Body Problem -- ยง 1. The Two-Body Problem -- ยง 2. Collisions and Regularization -- ยง 3. Particular Solutions -- ยง 4. Final Motions in the Three-Body Problem -- ยง 5. The Restricted Three-Body Problem -- ยง 6. Ergodic Theorems in Celestial Mechanics -- 3. Symmetry Groups and Reduction (Lowering the Order) -- ยง 1. Symmetries and Linear First Integrals -- ยง 2. Reduction of Systems with Symmetry -- ยง 3. Relative Equilibria and Bifurcations of Invariant Manifolds -- 4. Integrable Systems and Integration Methods -- ยง 1. Brief Survey of Various Approaches to the Integrability of Hamiltonian Systems -- ยง 2. Completely Integrable Systems -- ยง3. Some Methods of Integrating Hamiltonian Systems -- ยง4. Nonholonomic Integrable Systems -- 5. Perturbation Theory for Integrable Systems -- ยง1. Averaging of Perturbations -- ยง2. Averaging in Hamiltonian Systems -- ยง3. The KAM Theory -- ยง 4. Adiabatic Invariants -- 6. Nonintegrable Systems -- ยง1. Near-Integrable Hamiltonian Systems -- ยง 2. Splitting of Asymptotic Surfaces -- ยง 3. Quasi-Random Oscillations -- ยง 4. Nonintegrability in the Neighborhood of an Equilibrium Position (Siegelโ{128}{153}s Method) -- ยง 5. Branching of Solutions and Nonexistence of Single-Valued First Integrals -- ยง 6. Topological and Geometrical Obstructions to Complete Integrability of Natural Systems with Two Degrees of Freedom -- 7. Theory of Small Oscillations -- ยง1. Linearization -- ยง 2. Normal Forms of Linear Oscillations -- ยง 3. Normal Forms of Hamiltonian Systems Near Equilibria -- ยง 4. Normal Forms of Hamiltonian Systems Near Closed Trajectories -- ยง 5. Stability of Equilibria in Conservative Fields -- Comments on the Bibliography -- Recommended Reading

Mathematics Mathematical analysis Analysis (Mathematics) Physics Mathematics Analysis Theoretical Mathematical and Computational Physics


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