Mathematical Methods of Classical Mechanics

I Newtonian Mechanics. - 1 Experimental facts. - 2 Investigation of the equations of motion. - II Lagrangian Mechanics. - 3 Variational principles. - 4 Lagrangian mechanics on manifolds. - 5 Oscillations. - 6 Rigid bodies. - III Hamiltonian Mechanics. - 7 Differential forms. - 8 Symplectic manifolds. - 9 Canonical formalism. - 10 Introduction to perturbation theory. - Appendix 1 Riemannian curvature. - Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids. - Appendix 3 Symplectic structures on algebraic manifolds. - Appendix 4 Contact structures. - Appendix 5 Dynamical systems with symmetries. - Appendix 6 Normal forms of quadratic hamiltonians. - Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories. - Appendix 8 Theory of perturbations of conditionally periodic motion and Kolmogorov's theorem. - Appendix 9 Poincaré's geometric theorem its generalizations and applications. - Appendix 10 Multiplicities of characteristic frequencies and ellipsoids depending on parameters. - Appendix 11 Short wave asymptotics. - Appendix 12 Lagrangian singularities. - Appendix 13 The Korteweg-de Vries equation. - Appendix 14 Poisson structures. - Appendix 15 On elliptic coordinates. - Appendix 16 Singularities of ray systems. Language: English