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约束力学系统动力学（英文版）
作者：梅凤翔，吴惠彬 著
出版社：北京理工大学出版社
出版时间：2009-04-01
ISBN：9787564021689
定价：¥90.00
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内容简介
约束力学系统的变分原理、运动方程、相关专门问题的理论与应用、积分方法、对称性与守恒量等内容，具有很高的学术价值，为方便国际学术交流，译成英文出版。全书共分为六个部分：第一部分：约束力学系统的基本概念。本部分包含6章，介绍分析力学的主要基本概念；第二部分：约束力学系统的变分原理。本部分有5章，阐述微分变分原理、积分变分原理以及Pfaff-Birkhoff原理；第三部分：约束力学系统的运动微分方程。本部分共11章，系统介绍完整系统、非完整系统的各类运动方程；第四部分：约束力学系统的专门问题。本部分有8章，讨论运动稳定性和微扰理论、刚体定点转动、相对运动动力学、可控力学系统动力学、打击运动动力学、变质量系统动力学、机电系统动力学、事件空间动力学等内容；第五部分：约束力学系统的积分方法。本部分有6章，介绍降阶方法、动力学代数与Poisson方法、正则变换、Hamilton-Jacobi方法、场方法、积分不变量；第六部分：约束力学系统的对称性与守恒量。本部分共10章，讨论Noether对称性、Lie对称性、形式不变性，以及由它们导致的各种守恒量。《约束力学系统动力学（英文版）》的出版必将引起国内外同行的关注，对该领域的发展将起到重要的推动作用。
作者简介
Mei Fengxiang （1938-）， a native of Shenyang， China， and a graduate of the Department of Mathematics and Mechanics of Peking University （in 1963） and Ecole Nationalle Superiere de M6canique （Docteur dEtat， 1982）， has been teaching theoretical mechanics， analytical mechanics， dynamics of nonholonomic systems， stability of motion， and applications of Lie groups and Lie algebras to constrained mechanical systems at Beijing Institute of Technology. His research interests are in the areas of dynamics of constrained systems and mathematical methods in mechanics. He currently directs 12 doctoral candidates. He was a visiting professor at ENSM （1981-1982） and Universit LAVAL （1994）. Mei has authored over 300 research papers and is the author of the following 10 books （in Chinese）： Foundations of Mechanics of Nonholonomic Systems （1985）; Researches on Nonholonomic Dynamics （1987）; Foundations of Analytical Mechanics （1987）; Special Problems in Analytical Mechanics （1988）; Mechanics of Variable Mass Systems （1989）; Advanced Analytical Mechanics （1991）; Dynamics of Birkhoffian System （1996）; Stability of Motion of Constrained Mechanical Systems （1997）; Symmetries and Invariants of Mechanical Systems （1999）; and Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems （1999）.
目录
Ⅰ Fundamental Concepts in Constrained Mechanical Systems
1 Constraints and Their Classification
1.1 Constraints
1.2 Equations of Constraint
1.3 Classification of Constraints
1.3.1 Holonomic Constraints and Nonholonomic Constraints
1.3.2 Stationary Constraints and Non-stationary Constraints
1.3.3 Unilateral Constraints and Bilateral Constraints
1.3.4 Passive Constraints and Active Constraints
1.4 Integrability Theorem of Differential Constraints
1.5 Generalization of the Concept of Constraints
1.5.1 First Integral as Nonholonomic Constraints
1.5.2 Controllable System as Holonomic or Nonholonomic System
1.5.3 Nonholonomic Constraints of Higher Order
1.5.4 Restriction on Change of Dynamical Properties as Constraint
1.6 Remarks
2 Generalized Coordinates
2.1 Generalized Coordinates
2.2 Generalized Velocities
2.3 Generalized Accelerations
2.4 Expression of Equations of Nonholonomic Constraints in Terms of Generalized Coordinates and Generalized Velocities
2.5 Remarks
3 Quasi-Velocities and Quasi-Coordinates
3.1 Quasi-Velocities
3.2 Quasi-Coordinates
3.3 Quasi-Accelerations
3.4 Remarks
4 Virtual Displacements
4.1 Virtual Displacements
4.1.1 Concept of Virtual Displacements
4.1.2 Condition of Constraints Exerted on Virtual Displacements
4.1.3 Degree of Freedom
4.2 Necessary and Sufficient Condition Under Which Actual Displacement Is One of Virtual Displacements
4.3 Generalization of the Concept of Virtual Displacement
4.4 Remarks
5 Ideal Constraints
5.1 Constraint Reactions
5.2 Examples of Ideal Constraints
5.3 Importance and Possibility of Hypothesis of Ideal Constraints
5.4 Remarks
6 Transpositional Relations of Differential and Variational Operations
6.1 Transpositional Relations for First Order Nonholonomic Systems
6.1.1 Transpositional Relations in Terms of Generalized Coordinates
6.1.2 Transpositional Relations in Terms of Quasi-Coordinates
6.2 Transpositional Relations of Higher Order Nonholonomic Systems
6.2.1 Transpositional Relations in Terms of Generalized Coordinates
6.2.2 Transpositional Relations in Terms of Quasi-Coordinates
6.3 Vujanovic Transpositional Relations
6.3.1 Transpositional Relations for Holonomic Nonconservative Systems
6.3.2 Transpositional Relations for Nonholonomic Systems
6.4 Remarks
Ⅱ Variational Principles in Constrained Mechanical Systems
7 Differential Variational Principles
7.1 DAlembert-Lagrange Principle
7.1.1 DAlembert Principle
7.1.2 Principle of Virtual Displacements
7.1.3 DAlembert-Lagrange Principle
7.1.4 DAlembert-Lagrange Principle in
Terms of Generalized Coordinates
7.2 Jourdain Principle
7.2.1 Jourdain Principle
7.2.2 Jourdain Principle in Terms of Generalized Coordinates
7.3 Gauss Principle
7.3.1 Gauss Principle
7.3.2 Gauss Principle in Terms of Generalized Coordinates
7.4 Universal DAlerabert Principle
7.4.1 Universal DAlembert Principle
7.4.2 Universal DAlembert Principle in
Terms of Generalized Coordinates
7.5 Applications of Gauss Principle
7.5.1 Simple Applications
7.5.2 Application of Gauss Principle in Robot Dynamics
7.5.3 Application of Gauss Principle in Study Approximate Solution of Equations of Nonlinear Vibration
7.6 Remarks
8 Integral Variational Principles in Terms of Generalized Coordinates for Holonomic Systems
8.1 Hamiltons Principle
8.1.1 Hamiltons Principle
8.1.2 Deduction of Lagrange Equations
by Means of Hamiltons Principle
8.1.3 Character of Extreme of Hamiltons Principle
8.1.4 Applications in Finding Approximate Solution
8.1.5 Hamiltons Principle for General Holonomic Systems
8.2 Lagranges Principle
8.2.1 Non-contemporaneous Variation
8.2.2 Lagranges Principle
8.2.3 Other Forms of Lagranges Principle
8.2.4 Deduction of Lagrangcs Equations by Means of Lagranges Principle
8.2.5 Generalization of Lagranges Principle to Non-conservative Systems and Its Application
8.3 Remarks
9 Integral Variational Principles in Terms of Quasi-Coordinates for Holonomic Systems
9.1 Hamiltons Principle in Terms of Quasi-Coordinates
9.1.1 Hamiltons Principle
9.1.2 Transpositional Relations
9.1.3 Deduction of Equations of Motion in Terms of Quasi-Coordinates by Means of Hamiltons Principle
9.1.4 Hamiltons Principle for General Holonomic Systems
9.2 Lagranges Principle in Terms of Quasi-Coordinates
9.2.1 Lagranges Principle
9.2.2 Deduction of Equations of Motion in Terms of Quasi-Coordinates by Means of Lagranges Principle
9.3 Remarks
l0 Integral Variational Principles for Nonholonomic Systems
10.1 Definitions of Variation
10.1.1 Necessity of Definition of Variation of Generalized Velocities for Nonholonomic Systems
10.1.2 Suslovs Definition
10.1.3 HSlders Definition
10.2 Integral Variational Principles in Terms of Generalized Coordinates for Nonholonomic Systems
10.2.1 Hamiltons Principle for Nonholonomic Systems
10.2.2 Necessary and Sufficient Condition Under Which Hamiltons Principle for Nonholonomic Systems Is Principle of Stationary Action
10.2.3 Deduction of Equations of Motion for Nonholonomie Systems by Means of Hamiltons Principle
10.2.4 General Form of Hamiltons Principle for Nonhononomic Systems
10.2.5 Lagranges Principle in Terms of Generalized Coordinates for Nonholonomic Systems
10.3 Integral Variational Principle in Terms of QuasiCoordinates for Nonholonomic Systems
10.3.1 Hamiltons Principle in Terms of Quasi-Coordinates
10.3.2 Lagranges Principle in Terms of Quasi-Coordinates
10.4 Remarks
11 Pfaff-Birkhoff Principle
11.1 Statement of Pfaff-Birkhoff Principle
11.2 Hamiltons Principle as a Particular Case of Pfaff-Birkhoff Principle
11.3 Birkhoffs Equations
11.4 Pfaff-Birkhoff-dAlembert Principle
11.5 Remarks
III Differential Equations of Motion of Constrained Mechanical
Systems
12 Lagrange Equations of Holonomic Systems
12.1 Lagrange Equations of Second Kind
12.2 Lagrange Equations of Systems with Redundant Coordinates
12.3 Lagrange Equations in Terms of Quasi-Coordinates
12.4 Lagrange Equations with Dissipative Function
12.5 Remarks
13 Lagrange Equations with Multiplier for Nonholonomic Systems
13.1 Deduction of Lagrange Equations with Multiplier
13.2 Determination of Nonholonomic Constraint Forces
13.3 Remarks
14 Mac Millan Equations for Nonholonomie Systems
14.1 Deduction of Mac Millan Equations
14.2 Application of Mac MiUan Equations
14.3 Remarks
15 Volterra Equations for Nonholonomic Systems
15.1 Deduction of Generalized Volterra Equations
15.2 Volterra Equations and Their Equivalent Forms
15.2.1 Volterra Equations of First Form
15.2.2 Volterra Equations of Second Form
15.2.3 Volterra Equations of Third Form
15.2.4 Volterra Equations of Fourth Form
15.3 Application of Volterra Equations
15.4 Remarks
16 Chaplygin Equations for Nonholonomic Systems
16.1 Generalized Chaplygin Equations
16.2 Voronetz Equations
16.3 Chaplygin Equations
16.4 Chaplygin Equations in Terms of Quasi-Coordinates
16.5 Application of Chaplygin Equations
16.6 Remarks
……
Ⅳ Special Problems in Constrained Mechanical Systems
Ⅴ Integration Methods in Constrained Mechanical Systems
Ⅵ Symmetries and Conserved Quantities in Constrained Mechanical Systems
1 Constraints and Their Classification
1.1 Constraints
1.2 Equations of Constraint
1.3 Classification of Constraints
1.3.1 Holonomic Constraints and Nonholonomic Constraints
1.3.2 Stationary Constraints and Non-stationary Constraints
1.3.3 Unilateral Constraints and Bilateral Constraints
1.3.4 Passive Constraints and Active Constraints
1.4 Integrability Theorem of Differential Constraints
1.5 Generalization of the Concept of Constraints
1.5.1 First Integral as Nonholonomic Constraints
1.5.2 Controllable System as Holonomic or Nonholonomic System
1.5.3 Nonholonomic Constraints of Higher Order
1.5.4 Restriction on Change of Dynamical Properties as Constraint
1.6 Remarks
2 Generalized Coordinates
2.1 Generalized Coordinates
2.2 Generalized Velocities
2.3 Generalized Accelerations
2.4 Expression of Equations of Nonholonomic Constraints in Terms of Generalized Coordinates and Generalized Velocities
2.5 Remarks
3 Quasi-Velocities and Quasi-Coordinates
3.1 Quasi-Velocities
3.2 Quasi-Coordinates
3.3 Quasi-Accelerations
3.4 Remarks
4 Virtual Displacements
4.1 Virtual Displacements
4.1.1 Concept of Virtual Displacements
4.1.2 Condition of Constraints Exerted on Virtual Displacements
4.1.3 Degree of Freedom
4.2 Necessary and Sufficient Condition Under Which Actual Displacement Is One of Virtual Displacements
4.3 Generalization of the Concept of Virtual Displacement
4.4 Remarks
5 Ideal Constraints
5.1 Constraint Reactions
5.2 Examples of Ideal Constraints
5.3 Importance and Possibility of Hypothesis of Ideal Constraints
5.4 Remarks
6 Transpositional Relations of Differential and Variational Operations
6.1 Transpositional Relations for First Order Nonholonomic Systems
6.1.1 Transpositional Relations in Terms of Generalized Coordinates
6.1.2 Transpositional Relations in Terms of Quasi-Coordinates
6.2 Transpositional Relations of Higher Order Nonholonomic Systems
6.2.1 Transpositional Relations in Terms of Generalized Coordinates
6.2.2 Transpositional Relations in Terms of Quasi-Coordinates
6.3 Vujanovic Transpositional Relations
6.3.1 Transpositional Relations for Holonomic Nonconservative Systems
6.3.2 Transpositional Relations for Nonholonomic Systems
6.4 Remarks
Ⅱ Variational Principles in Constrained Mechanical Systems
7 Differential Variational Principles
7.1 DAlembert-Lagrange Principle
7.1.1 DAlembert Principle
7.1.2 Principle of Virtual Displacements
7.1.3 DAlembert-Lagrange Principle
7.1.4 DAlembert-Lagrange Principle in
Terms of Generalized Coordinates
7.2 Jourdain Principle
7.2.1 Jourdain Principle
7.2.2 Jourdain Principle in Terms of Generalized Coordinates
7.3 Gauss Principle
7.3.1 Gauss Principle
7.3.2 Gauss Principle in Terms of Generalized Coordinates
7.4 Universal DAlerabert Principle
7.4.1 Universal DAlembert Principle
7.4.2 Universal DAlembert Principle in
Terms of Generalized Coordinates
7.5 Applications of Gauss Principle
7.5.1 Simple Applications
7.5.2 Application of Gauss Principle in Robot Dynamics
7.5.3 Application of Gauss Principle in Study Approximate Solution of Equations of Nonlinear Vibration
7.6 Remarks
8 Integral Variational Principles in Terms of Generalized Coordinates for Holonomic Systems
8.1 Hamiltons Principle
8.1.1 Hamiltons Principle
8.1.2 Deduction of Lagrange Equations
by Means of Hamiltons Principle
8.1.3 Character of Extreme of Hamiltons Principle
8.1.4 Applications in Finding Approximate Solution
8.1.5 Hamiltons Principle for General Holonomic Systems
8.2 Lagranges Principle
8.2.1 Non-contemporaneous Variation
8.2.2 Lagranges Principle
8.2.3 Other Forms of Lagranges Principle
8.2.4 Deduction of Lagrangcs Equations by Means of Lagranges Principle
8.2.5 Generalization of Lagranges Principle to Non-conservative Systems and Its Application
8.3 Remarks
9 Integral Variational Principles in Terms of Quasi-Coordinates for Holonomic Systems
9.1 Hamiltons Principle in Terms of Quasi-Coordinates
9.1.1 Hamiltons Principle
9.1.2 Transpositional Relations
9.1.3 Deduction of Equations of Motion in Terms of Quasi-Coordinates by Means of Hamiltons Principle
9.1.4 Hamiltons Principle for General Holonomic Systems
9.2 Lagranges Principle in Terms of Quasi-Coordinates
9.2.1 Lagranges Principle
9.2.2 Deduction of Equations of Motion in Terms of Quasi-Coordinates by Means of Lagranges Principle
9.3 Remarks
l0 Integral Variational Principles for Nonholonomic Systems
10.1 Definitions of Variation
10.1.1 Necessity of Definition of Variation of Generalized Velocities for Nonholonomic Systems
10.1.2 Suslovs Definition
10.1.3 HSlders Definition
10.2 Integral Variational Principles in Terms of Generalized Coordinates for Nonholonomic Systems
10.2.1 Hamiltons Principle for Nonholonomic Systems
10.2.2 Necessary and Sufficient Condition Under Which Hamiltons Principle for Nonholonomic Systems Is Principle of Stationary Action
10.2.3 Deduction of Equations of Motion for Nonholonomie Systems by Means of Hamiltons Principle
10.2.4 General Form of Hamiltons Principle for Nonhononomic Systems
10.2.5 Lagranges Principle in Terms of Generalized Coordinates for Nonholonomic Systems
10.3 Integral Variational Principle in Terms of QuasiCoordinates for Nonholonomic Systems
10.3.1 Hamiltons Principle in Terms of Quasi-Coordinates
10.3.2 Lagranges Principle in Terms of Quasi-Coordinates
10.4 Remarks
11 Pfaff-Birkhoff Principle
11.1 Statement of Pfaff-Birkhoff Principle
11.2 Hamiltons Principle as a Particular Case of Pfaff-Birkhoff Principle
11.3 Birkhoffs Equations
11.4 Pfaff-Birkhoff-dAlembert Principle
11.5 Remarks
III Differential Equations of Motion of Constrained Mechanical
Systems
12 Lagrange Equations of Holonomic Systems
12.1 Lagrange Equations of Second Kind
12.2 Lagrange Equations of Systems with Redundant Coordinates
12.3 Lagrange Equations in Terms of Quasi-Coordinates
12.4 Lagrange Equations with Dissipative Function
12.5 Remarks
13 Lagrange Equations with Multiplier for Nonholonomic Systems
13.1 Deduction of Lagrange Equations with Multiplier
13.2 Determination of Nonholonomic Constraint Forces
13.3 Remarks
14 Mac Millan Equations for Nonholonomie Systems
14.1 Deduction of Mac Millan Equations
14.2 Application of Mac MiUan Equations
14.3 Remarks
15 Volterra Equations for Nonholonomic Systems
15.1 Deduction of Generalized Volterra Equations
15.2 Volterra Equations and Their Equivalent Forms
15.2.1 Volterra Equations of First Form
15.2.2 Volterra Equations of Second Form
15.2.3 Volterra Equations of Third Form
15.2.4 Volterra Equations of Fourth Form
15.3 Application of Volterra Equations
15.4 Remarks
16 Chaplygin Equations for Nonholonomic Systems
16.1 Generalized Chaplygin Equations
16.2 Voronetz Equations
16.3 Chaplygin Equations
16.4 Chaplygin Equations in Terms of Quasi-Coordinates
16.5 Application of Chaplygin Equations
16.6 Remarks
……
Ⅳ Special Problems in Constrained Mechanical Systems
Ⅴ Integration Methods in Constrained Mechanical Systems
Ⅵ Symmetries and Conserved Quantities in Constrained Mechanical Systems
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