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. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance. Preface
v
Preface to the Second edition
vii
Part I NEWTONIAN MECHANICS
1(52)
Experimental facts
3(12)
The principles of relativity and determinacy
3(1)
The galilean group and Newton's equations
4(7)
Examples of mechanical systems
11(4)
Investigation of the equations of motion
15(38)
Systems with one degree of freedom
15(7)
Systems with two degrees of freedom
22(6)
Conservative force fields
28(2)
Angular momentum
30(3)
Investigation of motion in a central field
33(9)
The motion of a point in three-space
42(2)
Motions of a system of n points
44(6)
The method of similarity
50(3)
Part II LAGRAGIAN MECHANICS
53(108)
Variational principles
55(20)
Calculus of variations
55(4)
Lagrange's equations
59(2)
Legendre transformations
61(4)
Hamilton's equations
65(3)
Liouville's theorem
68(7)
Lagrangian mechanics on manifolds
75(23)
Holonomic constraints
75(2)
Differentiable manifolds
77(6)
Lagragian dynamical systems
83(5)
E. Noether's theorem
88(3)
D'Alembert's principle
91(7)
Oscillations
98(25)
Linearization
98(5)
Small oscillations
103(7)
Behavior of characteristic frequencies
110(3)
Parametric resonance
113(10)
Rigid bodies
123(38)
Motion in a moving coordinate system
123(6)
Inertial forces and the Coriolis force
129(4)
Rigid bodies
133(9)
Euler's equations. Poinsot's description of the motion
142(6)
Language's top
148(6)
Sleeping tops and fast tops
154(7)
Part III HAMILTONIAN MECHANICS
161(140)
Differential forms
163(38)
Exterior forms
163(7)
Exterior multiplication
170(4)
Differential forms
174(7)
Integration of differential forms
181(7)
Exterior differentiation
188(13)
Symplectic manifolds
201(32)
Symplectic structures on manifolds
201(3)
Hamiltonian phase flows and their integral invariants
204(4)
The Lie algebra of vector fields
208(6)
The Lie algebra of hamiltonian functions
214(5)
Symplectic geometry
219(6)
Parametric resonance in systems with many degrees of freedom
225(4)
A symplectic atlas
229(4)
Canonical formalism
233(38)
The intergral invariant of Poincare-Cartan
233(7)
Applications of the integral invariant of Poincare-Cartan
240(8)
Huygens' principle
248(10)
The Hamilton- Jacobi method for integrating Hamilton's canonical equations
258(8)
Generating functions
266(5)
Introduction to perturbation theory
271(30)
Integrable systems
271(8)
Action- angle variables
279(6)
Averaging
285(6)
Averaging of perturbations
291(10)
Appendix 1 Riemannian curvature
301(17)
Appendix 2 Geodesics of left-invariant metrics on Lie groups and the hydrodynamics of ideal fluids
318(25)
Appendix 3 Symplectic structures on algebraic manifolds
343(6)
Appendix 4 Contact structures
349(22)
Appendix 5 Dynamical systems with symmetries
371(10)
Appendix 6 Normal forms of quadratic hamiltonians
381(4)
Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories
385(14)
Appendix 8 Theory of perturbations of conditionally periodic motion, and Kolmogorov's theorem
399(17)
Appendix 9 Poincare's geometric theorem, its generalizations and applications
416(9)
Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters
425(13)
Appendix 11 Short wave asymptotics
438(8)
Appendix 12 Lagrangian singularities
446(7)
Appendix 13 The Korteweg-de Vries equation
453(3)
Appendix 14 Poisson structures
456(13)
Appendix 15 On elliptic coordinates
469(11)
Appendix 16 Singularities of ray systems
480(31)
Index
511
Ik heb een vraag over het boek: ‘Mathematical Methods of Classical Mechanics - V. I. Arnold, K. Vogtmann, A. Weinstein’.
Vul het onderstaande formulier in.
We zullen zo spoedig mogelijk antwoorden.