Author | Arnold, V. I. author |
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Title | Mathematical Methods of Classical Mechanics [electronic resource] / by V. I. Arnold |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1989 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4757-2063-1 |
Descript | XVI, 520 p. online resource |
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 Kolmogorovโs theorem -- Appendix 9 Poincarรฉโs 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