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　　 《約束力學係統動力學（英文版）》共分46個章節，主要對約束力學係統的變分原理、運動方程、相關專門問題的理論與應用、積分方法、對稱性與守恒量等內容作瞭係統地闡述。該書可供各大專院校作為教材使用，也可供從事相關工作的人員作為參考用書使用。

內容簡介

　　 約束力學係統的變分原理、運動方程、相關專門問題的理論與應用、積分方法、對稱性與守恒量等內容，具有很高的學術價值，為方便國際學術交流，譯成英文齣版。全書共分為六個部分：第一部分：約束力學係統的基本概念。本部分包含6章，介紹分析力學的主要基本概念；第二部分：約束力學係統的變分原理。本部分有5章，闡述微分變分原理、積分變分原理以及Pfaff-Birkhoff原理；第三部分：約束力學係統的運動微分方程。本部分共11章，係統介紹完整係統、非完整係統的各類運動方程；第四部分：約束力學係統的專門問題。本部分有8章，討論運動穩定性和微擾理論、剛體定點轉動、相對運動動力學、可控力學係統動力學、打擊運動動力學、變質量係統動力學、機電係統動力學、事件空間動力學等內容；第五部分：約束力學係統的積分方法。本部分有6章，介紹降階方法、動力學代數與Poisson方法、正則變換、Hamilton-Jacobi方法、場方法、積分不變量；第六部分：約束力學係統的對稱性與守恒量。本部分共10章，討論Noether對稱性、Lie對稱性、形式不變性，以及由它們導緻的各種守恒量。《約束力學係統動力學（英文版）》的齣版必將引起國內外同行的關注，對該領域的發展將起到重要的推動作用。

作者簡介

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）.

目錄

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約束力學係統動力學（英文版） [Dynamics of Constrained Mechanical Systems] 下載 mobi epub pdf txt 電子書