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Mathematical aspects of classical and celestial mechanics /

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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...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Arnolʹd, V. I. (Vladimir Igorevich), 1937-2010, Kozlov, V. V., Neĭshtadt, A. I.
Format: eBook
Language:English
Published: Berlin ; New York : Springer, [1997]
Edition:Second edition.
Series:Dinamicheskie sistemy. 3.
Encyclopaedia of mathematical sciences ; v. 3.
Subjects:
Mechanics, Analytic.
Celestial mechanics.
Mécanique analytique.
Mécanique céleste.
Theoretische Mechanik.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. Basic Principles of Classical Mechanics
  • 1. Newtonian Mechanics
  • 2. Lagrangian Mechanics
  • 3. Hamiltonian Mechanics
  • 4. Vakonomic Mechanics
  • 5. Hamiltonian Formalism with Constraints
  • 6. Realization of Constraints
  • 2. The ?-Body Problem
  • 1. The Two-Body Problem
  • 2. Collisions and Regularization
  • 3. Particular Solutions
  • 4. Final Motions in the Three-Body Problem
  • 5. The Restricted Three-Body Problem
  • 6. Ergodic Theorems in Celestial Mechanics
  • 3. Symmetry Groups and Reduction (Lowering the Order)
  • 1. Symmetries and Linear First Integrals
  • 2. Reduction of Systems with Symmetry
  • 3. Relative Equilibria and Bifurcations of Invariant Manifolds
  • 4. Integrable Systems and Integration Methods
  • 1. Brief Survey of Various Approaches to the Integrability of Hamiltonian Systems
  • 2. Completely Integrable Systems
  • 3. Some Methods of Integrating Hamiltonian Systems
  • 4. Nonholonomic Integrable Systems
  • 5. Perturbation Theory for Integrable Systems
  • 1. Averaging of Perturbations
  • 2. Averaging in Hamiltonian Systems
  • 3. The KAM Theory
  • 4. Adiabatic Invariants
  • 6. Nonintegrable Systems
  • 1. Near-Integrable Hamiltonian Systems
  • 2. Splitting of Asymptotic Surfaces
  • 3. Quasi-Random Oscillations
  • 4. Nonintegrability in the Neighborhood of an Equilibrium Position (Siegels Method)
  • 5. Branching of Solutions and Nonexistence of Single-Valued First Integrals
  • 6. Topological and Geometrical Obstructions to Complete Integrability of Natural Systems with Two Degrees of Freedom
  • 7. Theory of Small Oscillations
  • 1. Linearization
  • 2. Normal Forms of Linear Oscillations
  • 3. Normal Forms of Hamiltonian Systems Near Equilibria
  • 4. Normal Forms of Hamiltonian Systems Near Closed Trajectories
  • 5. Stability of Equilibria in Conservative Fields
  • Comments on the Bibliography
  • Recommended Reading.