約束力學(xué)系統(tǒng)動(dòng)力學(xué)

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.

內(nèi)容概要

本書系統(tǒng)地闡述了約束力學(xué)系統(tǒng)的變分原理、運(yùn)動(dòng)方程、相關(guān)專門問題的理論與應(yīng)用、積分方法、對(duì)稱性與守恒量等內(nèi)容，具有很高的學(xué)術(shù)價(jià)值，為方便國際學(xué)術(shù)交流，譯成英文出版。全書共分為六個(gè)部分：    第一部分：約束力學(xué)系統(tǒng)的基本概念。本部分包含6章，介紹分析力學(xué)的主要基本概念；第二部分：約束力學(xué)系統(tǒng)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(xué)系統(tǒng)的運(yùn)動(dòng)微分方程。本部分共11章，系統(tǒng)介紹完整系統(tǒng)、非完整系統(tǒng)的各類運(yùn)動(dòng)方程；第四部分：約束力學(xué)系統(tǒng)的專門問題。本部分有8章，討論運(yùn)動(dòng)穩(wěn)定性和微擾理論、剛體定點(diǎn)轉(zhuǎn)動(dòng)、相對(duì)運(yùn)動(dòng)動(dòng)力學(xué)、可控力學(xué)系統(tǒng)動(dòng)力學(xué)、打擊運(yùn)動(dòng)動(dòng)力學(xué)、變質(zhì)量系統(tǒng)動(dòng)力學(xué)、機(jī)電系統(tǒng)動(dòng)力學(xué)、事件空間動(dòng)力學(xué)等內(nèi)容；第五部分：約束力學(xué)系統(tǒng)的積分方法。本部分有6章，介紹降階方法、動(dòng)力學(xué)代數(shù)與Poisson方法、正則變換、Hamilton-Jacobi方法、場(chǎng)方法、積分不變量；第六部分：約束力學(xué)系統(tǒng)的對(duì)稱性與守恒量。本部分共10章，討論Noether對(duì)稱性、Lie對(duì)稱性、形式不變性，以及由它們導(dǎo)致的各種守恒量。    本書的出版必將引起國內(nèi)外同行的關(guān)注，對(duì)該領(lǐng)域的發(fā)展將起到重要的推動(dòng)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 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）.

書籍目錄

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  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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《約束力學(xué)系統(tǒng)動(dòng)力學(xué)(英文版)》共分46個(gè)章節(jié)，主要對(duì)約束力學(xué)系統(tǒng)的變分原理、運(yùn)動(dòng)方程、相關(guān)專門問題的理論與應(yīng)用、積分方法、對(duì)稱性與守恒量等內(nèi)容作了系統(tǒng)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(guān)工作的人員作為參考用書使用。

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