Mathematical Aspects of Classical and Celestial Mechanics

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Main Authors: Arnold, V.I. (Editor), Kozlov, Victor V. (Author), Neishtadt, A.I. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1997, 1997
Edition:2nd ed. 1997
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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 (Siegel’s 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