LEADER 05570nam 2200733Ia 450 001 9910813336103321 005 20200520144314.0 010 $a0-19-152429-8 010 $a1-282-36571-1 010 $a1-4356-0925-5 010 $a9786612365713 035 $a(CKB)2560000000298302 035 $a(EBL)422625 035 $a(OCoLC)437109025 035 $a(SSID)ssj0000103054 035 $a(PQKBManifestationID)11117121 035 $a(PQKBTitleCode)TC0000103054 035 $a(PQKBWorkID)10060975 035 $a(PQKB)11723528 035 $a(StDuBDS)EDZ0000072444 035 $a(MiAaPQ)EBC422625 035 $a(Au-PeEL)EBL422625 035 $a(CaPaEBR)ebr10233645 035 $a(MiAaPQ)EBC3052611 035 $a(Au-PeEL)EBL3052611 035 $a(OCoLC)427509161 035 $a(EXLCZ)992560000000298302 100 $a20050822d2005 fy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalytical mechanics for relativity and quantum mechanics /$fOliver Davis Johns 205 $a1st ed. 210 $aOxford $cOxford University Press$d2005 215 $a1 online resource (618 p.) 225 1 $aOxford Graduate Texts 300 $aDescription based upon print version of record. 311 $a0-19-856726-X 311 $a0-19-171798-3 320 $aIncludes bibliographical references (p. 588-590) and index. 327 $aContents; Dedication; Preface; Acknowledgments; PART I: INTRODUCTION: THE TRADITIONAL THEORY; 1 Basic Dynamics of Point Particles and Collections; 1.1 Newton's Space and Time; 1.2 Single Point Particle; 1.3 Collective Variables; 1.4 The Law of Momentum for Collections; 1.5 The Law of Angular Momentum for Collections; 1.6 "Derivations" of the Axioms; 1.7 The Work-Energy Theorem for Collections; 1.8 Potential and Total Energy for Collections; 1.9 The Center of Mass; 1.10 Center of Mass and Momentum; 1.11 Center of Mass and Angular Momentum; 1.12 Center of Mass and Torque 327 $a1.13 Change of Angular Momentum1.14 Center of Mass and the Work-Energy Theorems; 1.15 Center of Mass as a Point Particle; 1.16 Special Results for Rigid Bodies; 1.17 Exercises; 2 Introduction to Lagrangian Mechanics; 2.1 Configuration Space; 2.2 Newton's Second Law in Lagrangian Form; 2.3 A Simple Example; 2.4 Arbitrary Generalized Coordinates; 2.5 Generalized Velocities in the q-System; 2.6 Generalized Forces in the q-System; 2.7 The Lagrangian Expressed in the q-System; 2.8 Two Important Identities; 2.9 Invariance of the Lagrange Equations; 2.10 Relation Between Any Two Systems 327 $a2.11 More of the Simple Example2.12 Generalized Momenta in the q-System; 2.13 Ignorable Coordinates; 2.14 Some Remarks About Units; 2.15 The Generalized Energy Function; 2.16 The Generalized Energy and the Total Energy; 2.17 Velocity Dependent Potentials; 2.18 Exercises; 3 Lagrangian Theory of Constraints; 3.1 Constraints Defined; 3.2 Virtual Displacement; 3.3 Virtual Work; 3.4 Form of the Forces of Constraint; 3.5 General Lagrange Equations with Constraints; 3.6 An Alternate Notation for Holonomic Constraints; 3.7 Example of the General Method; 3.8 Reduction of Degrees of Freedom 327 $a3.9 Example of a Reduction3.10 Example of a Simpler Reduction Method; 3.11 Recovery of the Forces of Constraint; 3.12 Example of a Recovery; 3.13 Generalized Energy Theorem with Constraints; 3.14 Tractable Non-Holonomic Constraints; 3.15 Exercises; 4 Introduction to Hamiltonian Mechanics; 4.1 Phase Space; 4.2 Hamilton Equations; 4.3 An Example of the Hamilton Equations; 4.4 Non-Potential and Constraint Forces; 4.5 Reduced Hamiltonian; 4.6 Poisson Brackets; 4.7 The Schroedinger Equation; 4.8 The Ehrenfest Theorem; 4.9 Exercises; 5 The Calculus of Variations; 5.1 Paths in an N-Dimensional Space 327 $a5.2 Variations of Coordinates5.3 Variations of Functions; 5.4 Variation of a Line Integral; 5.5 Finding Extremum Paths; 5.6 Example of an Extremum Path Calculation; 5.7 Invariance and Homogeneity; 5.8 The Brachistochrone Problem; 5.9 Calculus of Variations with Constraints; 5.10 An Example with Constraints; 5.11 Reduction of Degrees of Freedom; 5.12 Example of a Reduction; 5.13 Example of a Better Reduction; 5.14 The Coordinate Parametric Method; 5.15 Comparison of the Methods; 5.16 Exercises; 6 Hamilton's Principle; 6.1 Hamilton's Principle in Lagrangian Form 327 $a6.2 Hamilton's Principle with Constraints 330 $aThis book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It treats time as a transformable coordinate, and so moves the teaching of classical mechanics out of the ninteenth century and into the modern relativistic era. It also presents of classical mechanics in a way designed to assist the student's transition to quantum theory. - ;This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classic 410 0$aOxford Graduate Texts 606 $aMechanics, Analytic 606 $aQuantum theory 615 0$aMechanics, Analytic. 615 0$aQuantum theory. 676 $a530.11 676 $a531.01515 700 $aJohns$b Oliver Davis$0623101 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813336103321 996 $aAnalytical mechanics for relativity and quantum mechanics$91093674 997 $aUNINA