1 Basic Principles of Classical Mechanics 1 --
1.1 Newtonian Mechanics 1 --
1.2 Lagrangian Mechanics 17 --
1.3 Hamiltonian Mechanics 30 --
1.4 Vakonomic Mechanics 41 --
1.5 Hamiltonian Formalism with Constraints 48 --
1.6 Realization of Constraints 51 --
2.1 Two-Body Problem 61 --
2.2 Collisions and Regularization 72 --
2.3 Particular Solutions 79 --
2.4 Final Motions in the Three-Body Problem 83 --
2.5 Restricted Three-Body Problem 86 --
2.6 Ergodic Theorems of Celestial Mechanics 92 --
2.7 Dynamics in Spaces of Constant Curvature 95 --
3 Symmetry Groups and Order Reduction 103 --
3.1 Symmetries and Linear Integrals 103 --
3.2 Reduction of Systems with Symmetries 111 --
3.3 Relative Equilibria and Bifurcation of Integral Manifolds 126 --
4 Variational Principles and Methods 135 --
4.1 Geometry of Regions of Possible Motion 136 --
4.2 Periodic Trajectories of Natural Mechanical Systems 145 --
4.3 Periodic Trajectories of Non-Reversible Systems 156 --
4.4 Asymptotic Solutions. Application to the Theory of Stability of Motion 161 --
5 Integrable Systems and Integration Methods 171 --
5.1 Brief Survey of Various Approaches to Integrability of Hamiltonian Systems 171 --
5.2 Completely Integrable Systems 179 --
5.3 Some Methods of Integration of Hamiltonian Systems 191 --
5.4 Integrable Non-Holonomic Systems 199 --
6 Perturbation Theory for Integrable Systems 207 --
6.1 Averaging of Perturbations 207 --
6.2 Averaging in Hamiltonian Systems 256 --
6.4 Adiabatic Invariants 314 --
7 Non-Integrable Systems 351 --
7.1 Nearly Integrable Hamiltonian Systems 351 --
7.2 Splitting of Asymptotic Surfaces 360 --
7.3 Quasi-Random Oscillations 373 --
7.4 Non-Integrability in a Neighbourhood of an Equilibrium Position (Siegel's Method) 381 --
7.5 Branching of Solutions and Absence of Single-Valued Integrals 385 --
7.6 Topological and Geometrical Obstructions to Complete Integrability of Natural Systems 391 --
8 Theory of Small Oscillations 401 --
8.2 Normal Forms of Linear Oscillations 402 --
8.3 Normal Forms of Hamiltonian Systems near an Equilibrium Position 406 --
8.4 Normal Forms of Hamiltonian Systems near Closed Trajectories 417 --
8.5 Stability of Equilibria in Conservative Fields 422 --
9 Tensor Invariants of Equations of Dynamics 431 --
9.1 Tensor Invariants 431 --
9.2 Invariant Volume Forms 438 --
9.3 Tensor Invariants and the Problem of Small Denominators 445 --
9.4 Systems on Three-Dimensional Manifolds 451 --
9.5 Integral Invariants of the Second Order and Multivalued Integrals 455 --
9.6 Tensor Invariants of Quasi-Homogeneous Systems 457 --
9.7 General Vortex Theory 461.