Mathematical Methods of Classical Mechanics

基本信息

Series:Graduate Texts in Mathematics

Format:Hardback 520 pages, XVI, 520 p.

Publisher:Springer-Verlag New York Inc.

Imprint:Springer-Verlag New York Inc.

Edition:2nd ed. 1989. Corr. 4th printing 1997

ISBN:9780387968902

Published:5 Sep 1997

Weight:962g

Dimensions:237 x 162 x 35 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

本书从一开始就构建了经典力学的数学装置，研究了动力学中的基本问题，如振荡理论和哈密尔顿形式主义。作者强调了几何学方面的考虑，包括相空间和流、矢量场和李群。讨论包括动力系统理论的定性方法和渐进方法，如平均法和绝热不变性。

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.

目录

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.