目錄
Preface
Preface to the second edition
Part Ⅰ NEWTONIAN MECHANICS
Chapter 1 Experimental facts
1.The principles of relativity and determinacy
2.The galilean group and Newton's equations
3.Examples of mechanical systems
Chapter 2 Investigation of the equations of motion
4.Systems with one degree of freedom
5.Systems with two degrees of freedom
6.Conservative force felds
7.Angular momentum
8.Investigation of motion in a central feld
9.The motion of a point in three-space
10.Motions of a system of n points
11.The method of similarity
Part Ⅱ LAGRANGIAN MECHANICS
Chapter 3 Variational principles
12.Calculus of variations
13.Lagrange's equations
14.Legendre transformations
15.Hamilton's equations
16.Liouville's theorem
Chapter 4 Lagrangian mechanics on manifolds
17.Holonomic constraints
18.Diferentiable manifolds
19.Lagrangian dynamical systems
20.E.Noether's theorem
21.D'Alembert's principle
Chapter 5 Oscillations
22.Linearization
23.Small oscillations
24.Behavior of characteristic frequencies
25.Parametric resonance
Chapter 6 Rigid bodies
26.Motion in a moving coordinate system
27.Inertial forces and the Coriolis force
28.Rigid bodies
29.Euler's equations. Poinsot's description of the motion iteor lo eslqonn
30.Lagrange's top
31.Sleeping tops and fast tops
Part Ⅲ HAMILTONIAN MECHANICS
Chapter 7 Diferential forms
32.Exterior forms
33.Exterior multiplication
34.Differential forms
35.Integration of differential forms
36.Exterior differentiation
Chapter 8 Symplectic manifolds
37.Symplectic structures on manifolds
38.Hamiltonian phase flows and their integral invariants
39.The Lie algebra of vector fields
40.The Lie algebra of hamiltonian functions
41.Symplectic geometry
42.Parametric resonance in systems with many degrees of freedom
43.A symplectic atlas
Chapter 9 Canonical formalism
44.The integral invariant of Poincar? Cartan
45.Applications of the integral invariant of Poincar?-Cartan
46.Huygens' principle
47.The Hamilton-Jacobi method for integrating Hamilton's canonical equations
48.Generating functions
Chapter 10 Introduction to perturbation theory
49.Integrable systems
50.Action-angle variables
51.Averaging
52.Averaging of perturbations
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 Poincar?'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
Index
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