Author | Arnold, V. I. author |
---|---|
Title | Mathematical Aspects of Classical and Celestial Mechanics [electronic resource] / by V. I. Arnold, V. V. Kozlov, A. I. Neishtadt |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1997 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-61237-4 |
Descript | XIV, 294 p. online resource |
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 (Siegelโs 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