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1 Basic Principles of Classical Mechanics
1£®1 Newtonian Mechanics
1£®1£®1 Space£¬ Time£¬ Motion
1£®1£®2 Newton-Laplace Principle of Determinacy
1£®1£®3 Principle of Relativity
1£®1£®4 Principle of Relativity and Forces of Inertia
1£®1£®5 Basic Dynamical Quantities£® Conservation Laws
1£®2 Lagrangian Mechanics
1£®2£®1 Preliminary Remarks
1£®2£®2 Variations and Extremals
1£®2£®3 Lagrange's Equations
1£®2£®4 Poincare's Equations
1£®2£®5 Motion with Constraints
1£®3 Hamiltonian Mechanics
1£®3£®1 Symplectic Structures and Hamilton's Equations
1£®3£®2 Generating Functions
1£®3£®3 Symplectic Structure of the Cotangent Bundle
1£®3£®4 The Problem of n Point Vortices
1£®3£®5 Action in the Phase Space
1£®3£®6 Integral Invariant
1£®3£®7 Applications to Dynamics of Ideal Fluid
1£®4 Vakonomic Mechanics
1£®4£®1 Lagrange's Problem
1£®4£®2 Vakonomic Mechanics
1£®4£®3 Principle of Determinacy
1£®4£®4 Hamilton's Equations in Redundant Coordinates £®£®£®
1£®5 Hamiltonian Formalism with Constraints
1£®5£®1 Dirac's Problem
1£®5£®2 Duality
1£®6 Realization of Constraints
1£®6£®1 Various Methods of Realization of Constraints
1£®6£®2 Holonomic Constraints
1£®6£®3 Anisotropic Friction
1£®6£®4 Adjoint Masses
1£®6£®5 Adjoint Masses and Anisotropic Friction
1£®6£®6 Small Masses

2 The n-Body Problem
2£®1 The Two-Body Problem
2£®1£®1 Orbits
2£®1£®2 AnomMies
2£®1£®3 Collisions and Regularization
2£®1£®4 Geometry of Kepler's Problem
2£®2 Collisions and Regularization
2£®2£®1 Necessary Condition for Stability
2£®2£®2 Simultaneous Collisions
2£®2£®3 Binary Collisions
2£®2£®4 Singularities of Solutions of the n-Body Problem
2£®3 Particular Solutions
2£®3£®1 Central Configurations
2£®3£®2 Homographic Solutions
2£®3£®3 Effective Potential and Relative Equilibria
2£®3£®4 Periodic Solutions in the Case of Bodies of Equal Masses
2£®4 Final Motions in the Three-Body Problem
2£®4£®1 Classification of the Final Motions According to Chazy£®
2£®4£®2 Symmetry of the Past and Future ~£®
2£®5 Restricted Three-Body Problem
2£®5£®1 Equations of Motion£® The Jacobi Integral
2£®5£®2 Relative Equilibria and Hill Regions
2£®5£®3 Hill's Problem
2£®6 Ergodic Theorems of Celestial Mechanics
2£®6£®1 Stability in the Sense of Poisson
2£®6£®2 Probability of Capture
2£®7 Dynamics in Spaces of Constant Curvature
2£®7£®1 GenerMized Bertrand Problem
2£®7£®2 Kepler's Laws
2£®7£®3 Celestial Mechanics in Spaces of Constant Curvature
2£®7£®4 Potential Theory in Spaces of Constant Curvature

3 Symmetry Groups and Order Reduction
3£®1 Symmetries and Linear Integrals
3£®1£®1 NSther's Theorem
3£®1£®2 Symmetries in Non-Holonomic Mechanics
3£®1£®3 Symmetries in Vakonomic Mechanics
3£®1£®4 Symmetries in Hamiltonian Mechanics
3£®2 Reduction of Systems with Symmetries

3£®2£®1 Order Reduction £¨Lagrangian Aspect£©
3£®2£®2 Order Reduction £¨Hamiltonian Aspect£©
3£®2£®3 Examples£º Free Rotation of a Rigid Body and the Three-Body Problem
3£®3 Relative Equilibria and Bifurcation of Integral Manifolds
3£®3£®1 Relative Equilibria and Effective Potential
3£®3£®2 Integral Manifolds£¬ Regions of Possible Motion£¬ and Bifurcation Sets
3£®3£®3 The Bifurcation Set in the Planar Three-Body Problem
3£®3£®4 Bifurcation Sets and Integral Manifolds in theProblem of Rotation of a Heavy Rigid Body with a Fixed Point

4 Variational Principles and Methods
4£®1 Geometry of Regions of Possible Motion
4£®1£®1 Principle of Stationary Abbreviated Action
4£®1£®2 Geometry of a Neighbourhood of the Boundary
4£®1£®3 Riemannian Geometry of Regions of Possible Motion with Boundary
4£®2 Periodic Trajectories of Natural Mechanical Systems
4£®2£®1 Rotations and Librations
4£®2£®2 Librations in Non-Simply-Connected Regions of Possible Motion
4£®2£®3 Librations in Simply Connected Domains and Seifert's Conjecture
4£®2£®4 Periodic Oscillations of a Multi-Link Pendulum
4£®3 Periodic Trajectories of Non-Reversible Systems
4£®3£®1 Systems with Gyroscopic Forces and Multivalued Functionals
4£®3£®2 Applications of the Generalized Poincare Geometric Theorem
4£®4 Asymptotic Solutions£® Application to the Theory of Stability of Motion
4£®4£®1 Existence of Asymptotic Motions
4£®4£®2 Action Function in a Neighbourhood of an Unstable Equilibrium Position
4£®4£®3 Instability Theorem
4£®4£®4 Multi-Link Pendulum with Oscillating Point of Suspension
4£®4£®5 Homoclinic Motions Close to Chains of Homoclinic Motions

5 Integrable Systems and Integration Methods
5£®1 Brief Survey of Various Approaches to Integrability of Hamiltonian Systems
5£®1£®1 Quadratures
5£®1£®2 Complete Integrability
5£®1£®3 Normal Forms
5£®2 Completely Integrable Systems
5£®2£®1 Action-Angle Variables
5£®2£®2 Non-Commutative Sets of Integrals
5£®2£®3 Examples of Completely Integrable Systems
5£®3 Some Methods of Integration of Hamiltonian Systems
5£®3£®1 Method of Separation of Variables
5£®3£®2 Method of L-A Pairs
5£®4 Integrable Non-Holonomic Systems
5£®4£®1 Differential Equations with Invariant Measure
5£®4£®2 Some Solved Problems of Non-Holonomic Mechanics

6 Perturbation Theory for Integrable Systems
6£®1 Averaging of Perturbations
6£®1£®1 Averaging Principle
6£®1£®2 Procedure for Eliminating Fast Variables£® Non-Resonant Case
6£®1£®3 Procedure for Eliminating Fast Variables£® ResonantCase
6£®1£®4 Averaging in Single-Frequency Systems
6£®1£®5 Averaging inSystems with Constant Frequencies £®£®£®
6£®1£®6 Averaging in Non-Resonant Domains
6£®1£®7 Effect of a Single Resonance
6£®1£®8 Averaging in Two-Frequency Systems
6£®1£®9 Averaging in Multi-Frequency Systems
6£®1£®10 Averaging at Separatrix Crossing
6£®2 Averaging in Hamiltonian Systems
6£®2£®1 Application of the Averaging Principle
6£®2£®2 Procedures for Eliminating Fast Variables
6£®3 KAM Theory
6£®3£®1 Unperturbed Motion£® Non-Degeneracy Conditions
6£®3£®2 Invariant Tori of the Perturbed System
6£®3£®3 Systems with Two Degrees of Freedom
6£®3£®4 Diffusion of Slow Variables in Multidimensional
Systems and its Exponential Estimate
6£®3£®5 Diffusion without Exponentially Small Effects
6£®3£®6 Variants of the Theorem on Invariant Tori
6£®3£®7 KAM Theory for Lower-Dimensional Tori
6£®3£®8 Variational Principle for Invariant Tori£® Cantori
6£®3£®9 Applications of KAM Theory
6£®4 Adiabatic Invariants
6£®4£®1 Adiabatic Invariance of the Action Variable in Single-Frequency Systems
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7 Non-Integrable Systems
8 Theory of Small Oscillations
9 Tensor Invariants of Equations of Dynamics

Recommended Reading
Bibliography
Index of Names
Subject Index