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Cornelius Lanczos

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The Variational Principles of Mechanics

This chapter is in the book The Variational Principles of Mechanics

© 2020 University of Toronto Press, Toronto

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© 2020 University of Toronto Press, Toronto

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Chapters in this book

Frontmatter I
PREFACE VII
PREFACE TO THE SECOND EDITION XI
CONTENTS XIII
INTRODUCTION XVII
CHAPTER I. THE BASIC CONCEPTS OF ANALYTICAL MECHANICS 1
CHAPTER II. THE CALCULUS OF VARIATIONS 35
CHAPTER III. THE PRINCIPLE OF VIRTUAL WORK 74
CHAPTER IV. D'ALEMBERT'S PRINCIPLE 88
CHAPTER V. THE LAGRANGIAN EQUATIONS OF MOTION 111
CHAPTER VI. THE CANONICAL EQUATIONS OF MOTION 161
CHAPTER VII. CANONICAL TRANSFORMATIONS 193
CHAPTER VIII. THE PARTIAL DIFFERENTIAL EQUATION OF HAMILTON-JACOBI 229
CHAPTER IX. RELATIVISTIC MECHANICS 291
CHAPTER X. HISTORICAL SURVEY 341
APPENDIX 353
BIBLIOGRAPHY 357
INDEX 359

https://doi.org/10.3138/9781487583057-015

Chapters in this book

Frontmatter I
PREFACE VII
PREFACE TO THE SECOND EDITION XI
CONTENTS XIII
INTRODUCTION XVII
CHAPTER I. THE BASIC CONCEPTS OF ANALYTICAL MECHANICS 1
CHAPTER II. THE CALCULUS OF VARIATIONS 35
CHAPTER III. THE PRINCIPLE OF VIRTUAL WORK 74
CHAPTER IV. D'ALEMBERT'S PRINCIPLE 88
CHAPTER V. THE LAGRANGIAN EQUATIONS OF MOTION 111
CHAPTER VI. THE CANONICAL EQUATIONS OF MOTION 161
CHAPTER VII. CANONICAL TRANSFORMATIONS 193
CHAPTER VIII. THE PARTIAL DIFFERENTIAL EQUATION OF HAMILTON-JACOBI 229
CHAPTER IX. RELATIVISTIC MECHANICS 291
CHAPTER X. HISTORICAL SURVEY 341
APPENDIX 353
BIBLIOGRAPHY 357
INDEX 359

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