The Variational Principles of Mechanics / / Cornelius Lanczos.

• Superior document: Title is part of eBook package: De Gruyter University of Toronto Press eBook-Package Archive 1933-1999
• VerfasserIn: Lanczos, Cornelius,
• Place / Publishing House: Toronto : : University of Toronto Press, , [2020]; ©1949
• Year of Publication: 2020
• Language: English
• Series: Heritage
• Physical Description: 1 online resource (396 p.)

Analytical mechanics is much more than an efficient tool for the solution of dynamical problems encountered in physics and engineering. There is hardly a branch of the mathematical sciences in which abstract rigorous speculation and experimental evidence go together so beautifully and support each other so perfectly. Professor Lanczos's book is not a textbook on advances mechanics. Its purpose is to formulate and explain these fundamental concepts of this exact science which started with the work of Galileo and led to the achievements of modern relativity theory and quantum theory. "There is a tremendous treasure of philosophical meaning behind the great theories of Euler and Lagrange, and of Hamilton and Jacobi, which is complete smothered in a purely formalistic treatment," writes the author, "although it cannot fail to be a source of the greatest intellectual enjoyment to every mathematically minded person." To give the student a chance to discover for himself the hidden beauty of these theories was one of the foremost intentions of the author. He has led the reader through the entire historical development, included problems to familiarize the student with the new concepts and illustrate the general principles involved. For the most part, however, the author's aim is not to teach the solving of problems but rather to help the reader gain insight into the structure and significance of classical mechanics. The second edition adds a new chapter, "Relativistic Mechanics."

Table of Contents

Frontmatter -- PREFACE -- PREFACE TO THE SECOND EDITION -- CONTENTS -- INTRODUCTION -- CHAPTER I. THE BASIC CONCEPTS OF ANALYTICAL MECHANICS -- CHAPTER II. THE CALCULUS OF VARIATIONS -- CHAPTER III. THE PRINCIPLE OF VIRTUAL WORK -- CHAPTER IV. D'ALEMBERT'S PRINCIPLE -- CHAPTER V. THE LAGRANGIAN EQUATIONS OF MOTION -- CHAPTER VI. THE CANONICAL EQUATIONS OF MOTION -- CHAPTER VII. CANONICAL TRANSFORMATIONS -- CHAPTER VIII. THE PARTIAL DIFFERENTIAL EQUATION OF HAMILTON-JACOBI -- CHAPTER IX. RELATIVISTIC MECHANICS -- CHAPTER X. HISTORICAL SURVEY -- APPENDIX -- BIBLIOGRAPHY -- INDEX