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Analytical mechanics for relativity and quantum mechanics /
This work 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 is intended for use at the graduate level.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
2005.
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| Colección: | Oxford graduate texts.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""Cover""; ""Contents""; ""Dedication""; ""Prefaces""; ""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 Momentum""; ""1.14 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 Example""; ""2.12 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 Reduction""; ""3.10 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 From Lagrangian to Hamiltonian Mechanics""; ""4.8 Canonical Transformations""; ""4.9 Generating Functions""; ""4.10 The Schroedinger Equation""; ""4.11 The Ehrenfest Theorem""; ""4.12 The Virial Theorem""; ""4.13 Exercises""; ""5 The Calculus of Variations""; ""5.1 Paths in an N-Dimensional Space""; ""5.2 Variations of Coordinates""; ""5.3 Variations of Functions""; ""5.4 Variation of a Line Integral""