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　　分類: 图书,自然科学,力学,

作者：

出 版 社： 科学出版社

出版时间： 2009-1-1字数：版次： 1页数： 518印刷时间：开本： 16开印次：纸张：I S B N ： 9787030235077包装： 精装内容简介

This work describes the fundamental principles, problems, and methods of classical mechanics. The main attention is devoted to the mathematical side of the subject. The authors have endeavored to give an exposition stressing the working apparatus of classical mechanics. The book is significantly expanded compared to the previous edition. The authors have added two chapters on the variational principles and methods of classical mechanics as well as on tensor invariants of equations of dynamics. Moreover, various other sections have been revised, added or expanded. The main purpose of the book is to acquaint the reader with classical mechanics as a whole, in both its classical and its contemporary aspects.The book addresses all mathematicians, physicists and engineers.

目录

1 Basic Principles of Classical Mechanics

1.1 Newtonian Mechanics

1.1.1 Space, Time, Motion

1.1.2 Newton-Laplace Principle of Determinacy

1.1.3 Principle of Relativity

1.1.4 Principle of Relativity and Forces of Inertia

1.1.5 Basic Dynamical Quantities. Conservation Laws...

1.2 Lagrangian Mechanics

1.2.1 Preliminary Remarks

1.2.2 Variations and Extremals

1.2.3 Lagrange's Equations

1.2.4 Poincare's Equations

1.2.5 Motion with Constraints

1.3 Hamiltonian Mechanics

1.3.1 Symplectic Structures and Hamilton's Equations

1.3.2 Generating Functions

1.3.3 Symplectic Structure of the Cotangent Bundle

1.3.4 The Problem of n Point Vortices

1.3.5 Action in the Phase Space

1.3.6 Integral Invariant

1.3.7 Applications to Dynamics of Ideal Fluid

1.4 Vakonomic Mechanics

1.4.1 Lagrange's Problem

1.4.2 Vakonomic Mechanics

1.4.3 Principle of Determinacy

1.4.4 Hamilton's Equations in Redundant Coordinates

1.5 Hamiltonian Formalism with Constraints

1.5.1 Dirac's Problem

1.5.2 Duality '

1.6 Realization of Constraints

1.6.1 Various Methods of Realization of Constraints

1.6.2 Holonomic Constraints

1.6.3 Anisotropic Friction

1.6.4 Adjoint Masses

1.6.5 Adjoint Masses and Anisotropic Friction

1.6.6 Small Masses

2 The n-Body Problem

2.1 The Two-Body Problem

2.1.1 Orbits

2.1.2 Anomalies

2.1.3 Collisions and Regularization

2.1.4 Geometry of Kepler's Problem

2.2 Collisions and Regularization

2.2.1 Necessary Condition for Stability

2.2.2 Simultaneous Collisions

2.2.3 Binary Collisions

2.2.4 Singularities of Solutions of the n-Body Problem

2.3 Particular Solutions

2.3.1 Central Configurations

2.3.2 Homographic Solutions

2.3.3 Effective Potential and Relative Equilibria

2.3.4 Periodic Solutions in the Case of Bodies cf Equal Masses

2.4 Final Motions in the Three-Body Problem

2.4.1 Classification of the Final Motions According to Chazy.

2.4.2 Symmetry of the Past and Future

2.5 Restricted Three-Body Problem

2.5.1 Equations of Motion. The Jacobi Integral

2.5.2 Relative Equilibria and Hill Regions

2.5.3 Hill's Problem

2.6 Ergodic Theorems of Celestial Mechanics

2.6.1 Stability in the Sense of Poisson

2.6.2 Probability of Capture

2.7 Dynamics in Spaces of Constant Curvature

2.7.1 Generalized Bertrand Problem

2.7.2 Kepler's Laws

2.7.3 Celestial Mechanics in Spaces of Constant Curvature

2.7.4 Potential Theory in Spaces of Constant Curvature

3 Symmetry Groups and Order Reduction.

3.1 Symmetries and Linear Integrals

3.1.1 NSther's Theorem

3.1.2 Symmetries in Non-Holonomic Mechanics

3.1.3 Symmetries in Vakonomic Mechanics

3.1.4 Symmetries in Hamiltonian Mechanics

3.2 Reduction of Systems with Symmetries

……

4 Variational Principles and Methods

5 Integrable Systems and Integration Methods

6 Perturbation Theory for Integrable Systems

7 Non-Integrable Systems

8 Theory of Small Oscillations

9 Tensor Invariants of Equations of Dynamics

Recommended Reading

Bibliography

Index of Names

Subject Index

 

 

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