文档介绍：. Arnold (Ed.)
Dynamical SystemsIII
With 81 Figures
Springer-Verlag
Berlin Heidelberg NewYork
London Paris Tokyo
Encyclopaedia of
Mathematical Sciences
Volume 3
Editor-in-Chief: . Gamkrelidze
Mathematical Aspects
of Classical and Celestial Mechanics
. Arnold . Kozlov . Neishtadt
Translated from the Russian
by A. Iacob
Contents
Chapter 1. Basic Principles of Classical Mechanics . . . . . . . 1
9 1. Newtonian Mechanics ............. . . . . 1
. Space, Time, Motion ............ . . . . 1
. The Newton-Laplace Principle of Determinacy . . . . . 2
. The Principle of Relativity ......... . . . . 4
. Basic Dynamical Quantities. Conservation Laws . . 6
9 2. Lagrangian Mechanics ............. . . . . 9
. Preliminary Remarks ............ . . . . 9
. Variations and Extremals .......... . . . . 10
. Lagrange’s Equations ........... . . . . 12
. Poincart’s Equations ............ . . . . 13
. Constrained Motion ............ . . . . 16
4 3. Hamiltonian Mechanics ............ . . . . 20
. Symplectic Structures and Hamilton’s Equations . . 20
. Generating Functions ........... . . . . 22
. Symplectic Structure of the Cotangent Bundle . . . . . 23
. The Problem of 12Point Vortices ....... . . . . 24
. The Action Functional in Phase Space .... . . 26
. Integral Invariants ............. . . 27
. Applications to the Dynamics of Ideal Fluids . . . 29
. Principle of Stationary Isoenergetic Action . . . . 30
4 4. Vakonomic Mechanics ............. . . 31
. Lagrange’s Problem ............ . . 32
. Vakonomic Mechanics . . . . . . . . . . . . . . . . . 33
VIII Contents
. The Principle of Determinacy . . . . . . . . . . . . 36
. Hamilton’s Equations in Redundant Coordinates . . . . 37
4 5. Hamiltonian Formalism with Constraints . . . . . . . . . 38
. Dirac’s Problem . . . . . . . . . . . . . . . . .