Mathematical Methods of Classical Mechanics - Softcover

Arnold, V. I.

Softcover

ISBN 10: 147571694X ISBN 13: 9781475716948

Publisher: Springer, 2013

Synopsis

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 Geodesies of left-invariant metrics on Lie groups and the hydrodynamics of an ideal fluid.- Appendix 3 Symplectic structure 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 Perturbation theory of conditionally periodic motions 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.

Edition details

• Publisher: Springer
• Publication date: 2013
• Language: English
• ISBN 10: 147571694X
• ISBN 13: 9781475716948
• Binding: Paperback
• Number of pages: 476