Analytical mechanics for relativity and quantum mechanics [[electronic resource] /] / Oliver Davis Johns

• Autore: Johns Oliver Davis
• Pubblicazione: Oxford, : Oxford University Press, 2005
• Descrizione fisica: 1 online resource (618 p.)
• Disciplina: 530.11; 531.01515
• Soggetto topico: Mechanics, Analytic; Quantum theory
• Soggetto genere / forma: Electronic books.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 588-590) and index.
• Nota di contenuto: Contents; 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 ; 1.13 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 ; 2.11 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 ; 3.9 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 ; 5.2 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 ; 6.2 Hamilton's Principle with Constraints
• Sommario/riassunto: This 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
• Titolo autorizzato: Analytical mechanics for relativity and quantum mechanics
• ISBN: 0-19-152429-8; 1-282-36571-1; 1-4356-0925-5; 9786612365713
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910465790403321
• Lo trovi qui: Univ. Federico II
• Serie: Oxford Graduate Texts