The Variational Principles of Mechanics / Cornelius Lanczos.

Format:

Book

Author/Creator:

Lanczos, Cornelius, Author.

Series:

Mathematical expositions ; Number 4.

Heritage

Language:

English

Subjects (All):

Mechanics, Analytic.

Variational principles.

Physical Description:

1 online resource (395 pages).

Place of Publication:

Toronto : University of Toronto Press, [2020]

Language Note:

In English.

Summary:

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."

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

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 05. Mai 2020)

ISBN:

1-4875-8305-2

OCLC:

1153480888