经典力学的现代方法/MODERN APPROACH TO CLASSICAL MECHANICS, A
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作者： Harald IrO 著
出 版 社： Pengiun Group (USA)
出版时间： 2002-12-1字数：版次： 1页数： 442印刷时间： 2003/01/01开本：印次：纸张： 胶版纸I S B N ： 9789812382139包装： 精装内容简介
This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community.
目录
1Introduction
1.1 Classical mechanics is challenging again
1.2 On the scientific method
1.3 Time, space and motion
2The foundations of mechanics
2.1 Newton's laws
2.1.1 Mass, quantity of motion and force
2.1.2 The fundamental laws of classical mechanics
2.1.3 Mechanics of a point mass
2.2 First integrals of Newton's equation of motion
2.2.1 Constants of motion and conserved quantities
2.2.2 Conservation of energy
2.2.3 Angular momentum and its conservation
3One-dimensional motion of a particle
3.1 Examples of one-dimensional motion
3.2 General features
3.3 The inclined track
3.4 The plane pendulum
3.5 The harmonic oscillator
3.6 The driven, damped oscillator
3.6.1 The driven oscillator with linear damping
3.6.2 The periodically driven, damped oscillator
3.7 Stability of motion
3.7.1 Two examples
3.7.2 Linear stability analysis
3.8 Anharmonic one-dimensional motion
4 Encountering peculiar motion in two dimensions
4.1 The two-dimensional harmonic oscillator
4.2 The Henon-Heiles system
4.3 A 'useless' conserved quantity
4.4 Chaotic behavior
4.5 Laplace's clock mechanism does not exist
5 Motion in a central force field
5.1 General features of the motion
5.1.1 Conserved quantities
5.1.2 The effective potential
5.1.3 Properties of the orbits
5.2 Motion in a 1/r potential
5.2.1 The caseL≠0
5.2.2 Bounded motion for L = 0
5.3 Motion in the potential V（r） ∝ 1/ra
5.3.1 Mechanical similarity
5.4 The Runge-Lenz vector
5.5 Integrability vanishes
5.5.1 The homogeneous magnetic field as the sole force
5.5.2 Addition of a central force
5.5.3 Motion in the symmetry plane
6The gravitational interaction of two bodies
6.1 Two-body systems
6.1.1 Center of mass and relative coordinates
6.1.2 Conserved quantities
6.2The gravitational interaction
6.3Kepler's laws
6.4The gravitational potential of a body of finite size
6.4.1 The potential of a homogeneous sphere
6.4.2 The potential of an inhomogeneous body...
6.5On the validity of the gravitational law
7Collisions of particles. Scattering
7.1 Unbounded motion in a central force field
7.2 Kinematics of two-particle-collisions
7.2.1 Elastic collisions of two particles
7.2.2 Kinematics of elastic collisions
……
8 Changing the frame of reference
9 Lagrangian mechanics
10 Conservation laws and symmetries in many particlesystems
11The rigid body
12Small oscillations
13Hamilton's canonical formulation of mechanics
14 Hamilton-Jacobi theory
15 From integrable to non-integrable systems
In retrospect
Appendix
A Coordinate systems and some vector analysis
B Rotations and tensors
C Green`s functions
Bibliography
Index
