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）.
圖書目錄
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 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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