约束力学系统动力学-英文版 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 D'Alembert-Lagrange Principle
7.1.1 D'Alembert Principle
7.1.2 Principle of Virtual Displacements
7.1.3 D'Alembert-Lagrange Principle
7.1.4 D'Alembert-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 D'Alerabert Principle
7.4.1 Universal D'Alembert Principle
7.4.2 Universal D'Alembert 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 Hamilton's Principle
8.1.1 Hamilton's Principle
8.1.2 Deduction of Lagrange Equations
by Means of Hamilton's Principle
8.1.3 Character of Extreme of Hamilton's Principle
8.1.4 Applications in Finding Approximate Solution
8.1.5 Hamilton's Principle for General Holonomic Systems
8.2 Lagrange's Principle
8.2.1 Non-contemporaneous Variation
8.2.2 Lagrange's Principle
8.2.3 Other Forms of Lagrange's Principle
8.2.4 Deduction of Lagrangc's Equations by Means of Lagrange's Principle
8.2.5 Generalization of Lagrange's 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 Hamilton's Principle in Terms of Quasi-Coordinates
9.1.1 Hamilton's Principle
9.1.2 Transpositional Relations
9.1.3 Deduction of Equations of Motion in Terms of Quasi-Coordinates by Means of Hamilton's Principle
9.1.4 Hamilton's Principle for General Holonomic Systems

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