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| 1 basic principles of classical mechanics . 1.1 newtonian mechanics 1.2 lagrangian mechanics 1.3 hamiltonian mechanics 1.4 vakonomic mechanics 1.5 hamiltonian formalism with constraints 1.6 realization of constraints 2 the n-body problem 2.1 the two-body problem 2.2 collisions and regularization 2.3 particular solutions 2.4 final motions in the three-body problem 2.5 restricted three-body problem 2.6 ergodic theorems of celestial mechanics 2.7 dynamics in spaces of constant curvature 3 symmetry groups and order reduction 3.1 symmetries and linear integrals 3.2 reduction of systems with symmetries 3.3 relative equilibria and bifurcation of integral manifolds 4 variational principles and methods .4.1 geometry of regions of possible motion 4.2 periodic trajectories of natural mechanical systems 4.3 periodic trajectories of non-reversible systems 4.4 asymptotic solutions. application to the theory of stability of motion 5 integrable systems and integration methods 5.1 brief survey of various approaches to integrability of hamiltonian systems 5.2 completely integrable systems 5.3 some methods of integration of hamiltonian systems 5.4 integrable non-holonomic systems 6 perturbation theory for integrable systems .. 6.1 averaging of perturbations 6.2 averaging in hamiltonian systems 6.3 kam theory 6.4 adiabatic invariants 7 non-integrable systems 7.1 nearly integrable hamiltonian systems 7.2 splitting of asymptotic surfaces 7.3 quasi-random oscillations 7.4 non-integrability in a neighbourhood of an equilibrium position (siegel's method) 7.5 branching of solutions and absence of single-valued integrals 7.6 topological and geometrical obstructions to complete integrability of natural systems 8 theory of small oscillations 8.1 linearization 8.2 normal forms of linear oscillations 8.3 normal forms of hamiltonian systems near an equilibrium position 8.4 normal forms of hamiltonian systems near closed trajectories 8.5 stability of equilibria in conservative fields 9 tensor invariants of equations of dynamics 9.1 tensor invariants 9.2 invariant volume forms 9.3 tensor invariants and the problem of small denominators 9.4 systems on three-dimensional manifolds 9.5 integral invariants of the second order and multivalued integrals 9.6 tensor invariants of quasi-homogeneous systems 9.7 general vortex theory recommended reading bibliography index of names subject index ... |
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