約束力學系統動力學

約束力學系統動力學

图书基本信息
出版时间:2009-4
出版社:北京理工大學出版社
作者:梅鳳翔,吳惠彬 著
页数:604
书名:約束力學系統動力學
封面图片
約束力學系統動力學
前言
This book is entitled Dynamics of Constrained Mechanical Systems. The constrained mechanical systems,in my opinion,contain the three kinds of the systems, i.e. the holonomic systems, the nonholonomic systems and the Birkhoff systems. The book covers the following six parts.Part I  Fundamental Concepts in Constrained Mechanical Systems. The part has 6 chapters: Constraints and their classification, Generalized coordinates, Quasi-velocities and quasicoordinates, Virtual displacements, Ideal constraints, Transpositional relations of differential and variational operators.Part II Variational Principles in Constrained Mechanical Systems. It covers 5 chapters: Differential variational principles, Integral variational principles in terms of generalized coordinates for holonomic systems, Integral variational principles in terms of quasi-coordinates for holonomic systems, Integral variational principles for nonholonomic systems, Pfaff-Birkhoff principle.Part III  Differential Equations of Motion of Constrained Mechanical Systems. It covers 11 chapters: Lagrange equations of holonomic systems, Lagrange equations with multiplier for nonholonomic systems, Mac Millan equations for nonholonomic systems, Volterra equations for nonholonomic systems, Chaplygin equations for nonholonomic systems, Boltzmann-Hamel equations for nonholonomic systems, Euler-Lagrange equations for higher order honholonomic systems, Nielsen equations, Appell equations, Equations of motion of mixed type, Canonical equations.Part IV Special Problems in Constrained Mechanical Systems. It covers 8 chapters: Stability of motion and theory of small oscillations, Dynamics of rigid body with fixed point, Dynamics of relative motion, Dynamics of controllable mechanical systems, Dynamics of impulsive motion, Dynamics of variable mass systems, Dynamics of electromechanical systems, Dynamics in event space.Part V  Integration Methods in Constrained Mechanical Systems. It covers 6 chapters: Methods of reduction of order, Dynamics algebra and Poisson method, Canonical transformations, Hamilton-Jacobi method, Field method, Integral invariants.Part VI  Symmetries and Conserved Quantities in Constrained Mechanical Systems. The part has 10 chapters: Noether symmetries and conserved quantities, Lie symmetries and Hojman conserved quantities, Form invariance and new conserved quantities, Noether symmetries and Hojman conserved quantities, Noether symmetries and new conserved quantities, Lie symmetries and Noether conserved quantities~ Lie symmetries and new conserved quantities, Form invariance and Noether conserved quantities, Form invariance and Hojman conserved quantities, Unified symmetries and conserved quantities.
内容概要
本書系統地闡述了約束力學系統的變分原理、運動方程、相關專門問題的理論與應用、積分方法、對稱性與守恆量等內容,具有很高的學術價值,為方便國際學術交流,譯成英文出版。全書共分為六個部分︰    第一部分︰約束力學系統的基本概念。本部分包含6章,介紹分析力學的主要基本概念;第二部分︰約束力學系統的變分原理。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︰約束力學系統的運動微分方程。本部分共11章,系統介紹完整系統、非完整系統的各類運動方程;第四部分︰約束力學系統的專門問題。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、可控力學系統動力學、打擊運動動力學、變質量系統動力學、機電系統動力學、事件空間動力學等內容;第五部分︰約束力學系統的積分方法。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︰約束力學系統的對稱性與守恆量。本部分共10章,討論Noether對稱性、Lie對稱性、形式不變性,以及由它們導致的各種守恆量。    本書的出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 d'Etat, 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).
书籍目录
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  RemarksⅡ  Variational Principles in Constrained Mechanical Systems 7  Differential Variational Principles   7.1  D'Alembert-Lagrange Principle  ……Ⅲ  Differential Equations of Motion of Constrained Mechanical SystemsⅣ  Special Problems in Constrained Mechanical SystemsⅤ  Integration Methods in Constrained Mechanical SystemsⅥ  Symmetries and Conserved Quantities in Constrained Mechanical Systems
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编辑推荐
《約束力學系統動力學(英文版)》共分46個章節,主要對約束力學系統的變分原理、運動方程、相關專門問題的理論與應用、積分方法、對稱性與守恆量等內容作了系統地闡述。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。
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