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book: Mechanics in Differential Geometry
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Mechanics in Differential Geometry

Language: English
Published/Copyright: 2006
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    i-vi

    i
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    CONTENTS

    vii
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    PREFACE

    xv
    Yves R. Talpaert
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  • CHAPTER Ο. INTRODUCTION TO TENSORS
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    1. WELL KNOWN CONCEPTS

    1
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    2. OPERATIONS ON TENSORS

    19
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  • CHAPTER 1. FOUNDATIONS OF DIFFERENTIAL GEOMETRY
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    1. MANIFOLDS

    25
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    2. TANGENT VECTOR SPACE

    42
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    3. TANGENT BUNDLE, VECTOR FIELD, AND LIE ALGEBRA

    59
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    4. COTANGENT BUNDLE AND COVECTOR FIELDS

    75
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    5. TENSOR ALGEBRA AND TENSOR FIELDS

    83
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    6. EXTERIOR DIFFERENTIAL FORMS

    94
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    7. LIE DERIVATIVE, LIE GROUP, AND LIE ALGEBRA

    122
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    8. INTEGRATION OF FORMS

    173
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    9. RIEMANNIAN GEOMETRY

    192
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    EXERCISES

    234
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  • CHAPTER 2. SYMPLECTIC GEOMETRY
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    1. PRELIMINARIES

    253
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    2. SYMPLECTIC GEOMETRY

    258
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  • CHAPTER 3. A MODERN EXPOSITION OF MECHANICS
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    1. LAGRANGIAN MECHANICS

    285
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    2. HAMILTONIAN MECHANICS

    306
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    3. COMPARISON OF THE LAGRANGIAN AND HAMILTONIAN FORMULATIONS

    334
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    4. HAMILTON–JACOBI MECHANICS

    370
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    5. INTRODUCTION TO PERTURBATIONS

    409
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    EXERCISES

    460
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  • CHAPTER 4. THE N-BODY PROBLEM; AN ORIGINAL METHOD FOR LARGE Ν
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    1. N-BODY PROBLEM, EQUATIONS AND INTEGRALS

    481
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    2. THE N-BODY PROBLEM IN STATISTICAL MECHANICS

    523
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    BIBLIOGRAPHY

    553
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    GLOSSARY OF SYMBOLS

    557
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    INDEX

    563
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
March 20, 2012
eBook ISBN:
9783110917796
Pages and Images/Illustrations in book
Front matter:
17
Main content:
571
https://doi.org/10.1515/9783110917796
eBook ISBN: 9783110917796
Keywords for this book
Differentialgeometrie
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