Mathematical methods of classical mechanics
著者
書誌事項
Mathematical methods of classical mechanics
（Graduate texts in mathematics, 60）
Springer-Verlag, c1989
2nd ed
- : us
- : gw
- タイトル別名
-
Matematicheskie metody klassicheskoĭ mekhaniki
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注記
"Title of the Russian original edition: Matematicheskie metody klassicheskoĭ mekhaniki. Nauka, Moscow, 1974"--T.p. verso. Originally published: Moscow : Nauka, 1974
Originally published as Mathematical methods of classical mechanics: New York : Springer, 1978
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387968902
内容説明
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
目次
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 Poincare'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.
- 巻冊次
-
: gw ISBN 9783540968900
内容説明
In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
目次
- Part 1 Newtonian mechanics: experimental facts
- investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles
- Lagrangian mechanics on manifolds
- oscillations
- rigid bodies. Part 3 Hamiltonian mechanics: differential forms
- symplectic manifolds
- canonical formalism
- introduction to pertubation theory.
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