约束力学系统动力学-英文版

目录

Ⅰ Fundamental Concepts in Constrained Mechanical Systems1 Constraints and Their Classification1.1 Constraints1.2 Equations of Constraint1.3 Classification of Constraints1.3.1 Holonomic Constraints and Nonholonomic Constraints1.3.2 Stationary Constraints and Non-stationary Constraints1.3.3 Unilateral Constraints and Bilateral Constraints1.3.4 Passive Constraints and Active Constraints1.4 Integrability Theorem of Differential Constraints1.5 Generalization of the Concept of Constraints1.5.1 First Integral as Nonholonomic Constraints1.5.2 Controllable System as Holonomic or Nonholonomic System1.5.3 Nonholonomic Constraints of Higher Order1.5.4 Restriction on Change of Dynamical Properties as Constraint1.6 Remarks2 Generalized Coordinates2.1 Generalized Coordinates2.2 Generalized Velocities2.3 Generalized Accelerations2.4 Expression of Equations of Nonholonomic Constraints in Terms of Generalized Coordinates and Generalized Velocities2.5 Remarks3 Quasi-Velocities and Quasi-Coordinates3.1 Quasi-Velocities3.2 Quasi-Coordinates3.3 Quasi-Accelerations3.4 Remarks4 Virtual Displacements4.1 Virtual Displacements4.1.1 Concept of Virtual Displacements4.1.2 Condition of Constraints Exerted on Virtual Displacements4.1.3 Degree of Freedom4.2 Necessary and Sufficient Condition Under Which Actual Displacement Is One of Virtual Displacements4.3 Generalization of the Concept of Virtual Displacement4.4 Remarks5 Ideal Constraints5.1 Constraint Reactions5.2 Examples of Ideal Constraints5.3 Importance and Possibility of Hypothesis of Ideal Constraints5.4 Remarks6 Transpositional Relations of Differential and Variational Operations6.1 Transpositional Relations for First Order Nonholonomic Systems6.1.1 Transpositional Relations in Terms of Generalized Coordinates6.1.2 Transpositional Relations in Terms of Quasi-Coordinates6.2 Transpositional Relations of Higher Order Nonholonomic Systems6.2.1 Transpositional Relations in Terms of Generalized Coordinates6.2.2 Transpositional Relations in Terms of Quasi-Coordinates6.3 Vujanovic Transpositional Relations6.3.1 Transpositional Relations for Holonomic Nonconservative Systems6.3.2 Transpositional Relations for Nonholonomic Systems6.4 RemarksⅡ Variational Principles in Constrained Mechanical Systems7 Differential Variational Principles7.1 D’Alembert-Lagrange Principle7.1.1 D’Alembert Principle7.1.2 Principle of Virtual Displacements7.1.3 D’Alembert-Lagrange Principle7.1.4 D’Alembert-Lagrange Principle inTerms of Generalized Coordinates7.2 Jourdain Principle7.2.1 Jourdain Principle7.2.2 Jourdain Principle in Terms of Generalized Coordinates7.3 Gauss Principle7.3.1 Gauss Principle7.3.2 Gauss Principle in Terms of Generalized Coordinates7.4 Universal D’Alerabert Principle7.4.1 Universal D’Alembert Principle7.4.2 Universal D’Alembert Principle inTerms of Generalized Coordinates7.5 Applications of Gauss Principle7.5.1 Simple Applications7.5.2 Application of Gauss Principle in Robot Dynamics7.5.3 Application of Gauss Principle in Study Approximate Solution of Equations of Nonlinear Vibration7.6 Remarks8 Integral Variational Principles in Terms of Generalized Coordinates for Holonomic Systems8.1 Hamilton’s Principle8.1.1 Hamilton’s Principle8.1.2 Deduction of Lagrange Equationsby Means of Hamilton’s Principle8.1.3 Character of Extreme of Hamilton’s Principle8.1.4 Applications in Finding Approximate Solution8.1.5 Hamilton’s Principle for General Holonomic Systems8.2 Lagrange’s Principle8.2.1 Non-contemporaneous Variation8.2.2 Lagrange’s Principle8.2.3 Other Forms of Lagrange’s Principle8.2.4 Deduction of Lagrangc’s Equations by Means of Lagrange’s Principle8.2.5 Generalization of Lagrange’s Principle to Non-conservative Systems and Its Application8.3 Remarks9 Integral Variational Principles in Terms of Quasi-Coordinates for Holonomic Systems9.1 Hamilton’s Principle in Terms of Quasi-Coordinates9.1.1 Hamilton’s Principle9.1.2 Transpositional Relations9.1.3 Deduction of Equations of Motion in Terms of Quasi-Coordinates by Means of Hamilton’s Principle9.1.4 Hamilton’s Principle for General Holonomic Systems9.2 Lagrange’s Principle in Terms of Quasi-Coordinates9.2.1 Lagrange’s Principle9.2.2 Deduction of Equations of Motion in Terms of Quasi-Coordinates by Means of Lagrange’s Principle9.3 Remarksl0 Integral Variational Principles for Nonholonomic Systems10.1 Definitions of Variation10.1.1 Necessity of Definition of Variation of Generalized Velocities for Nonholonomic Systems10.1.2 Suslov’s Definition10.1.3 HSlder’s Definition10.2 Integral Variational Principles in Terms of Generalized Coordinates for Nonholonomic Systems10.2.1 Hamilton’s Principle for Nonholonomic Systems10.2.2 Necessary and Sufficient Condition Under Which Hamilton’s Principle for Nonholonomic Systems Is Principle of Stationary Action10.2.3 Deduction of Equations of Motion for Nonholonomie Systems by Means of Hamilton’s Principle10.2.4 General Form of Hamilton’s Principle for Nonhononomic Systems10.2.5 Lagranges Principle in Terms of Generalized Coordinates for Nonholonomic Systems10.3 Integral Variational Principle in Terms of QuasiCoordinates for Nonholonomic Systems10.3.1 Hamilton’s Principle in Terms of Quasi-Coordinates10.3.2 Lagrange’s Principle in Terms of Quasi-Coordinates10.4 Remarks11 Pfaff-Birkhoff Principle11.1 Statement of Pfaff-Birkhoff Principle11.2 Hamilton’s Principle as a Particular Case of Pfaff-Birkhoff Principle11.3 Birkhoff’s Equations11.4 Pfaff-Birkhoff-d’Alembert Principle11.5 RemarksIII Differential Equations of Motion of Constrained MechanicalSystems12 Lagrange Equations of Holonomic Systems12.1 Lagrange Equations of Second Kind12.2 Lagrange Equations of Systems with Redundant Coordinates12.3 Lagrange Equations in Terms of Quasi-Coordinates12.4 Lagrange Equations with Dissipative Function12.5 Remarks13 Lagrange Equations with Multiplier for Nonholonomic Systems13.1 Deduction of Lagrange Equations with Multiplier13.2 Determination of Nonholonomic Constraint Forces13.3 Remarks14 Mac Millan Equations for Nonholonomie Systems14.1 Deduction of Mac Millan Equations14.2 Application of Mac MiUan Equations14.3 Remarks15 Volterra Equations for Nonholonomic Systems15.1 Deduction of Generalized Volterra Equations15.2 Volterra Equations and Their Equivalent Forms15.2.1 Volterra Equations of First Form15.2.2 Volterra Equations of Second Form15.2.3 Volterra Equations of Third Form15.2.4 Volterra Equations of Fourth Form15.3 Application of Volterra Equations15.4 Remarks16 Chaplygin Equations for Nonholonomic Systems16.1 Generalized Chaplygin Equations16.2 Voronetz Equations16.3 Chaplygin Equations16.4 Chaplygin Equations in Terms of Quasi-Coordinates16.5 Application of Chaplygin Equations16.6 Remarks……Ⅳ Special Problems in Constrained Mechanical SystemsⅤ Integration Methods in Constrained Mechanical SystemsⅥ Symmetries and Conserved Quantities in Constrained Mechanical Systems

封面

书名:约束力学系统动力学-英文版

作者:梅凤翔.吴惠彬著

页数:604 页

定价:¥90.0

出版社:北京理工大学出版社

出版日期:2009-04-01

ISBN:9787564021689

PDF电子书大小:45MB 高清扫描完整版