The Variational Principles of Mechanics
Analytical mechanics is, of course, a topic of perennial interest and usefulness in physics and engineering, a discipline that boasts not only many practical applications, but much inherent mathematical beauty. Unlike many standard textbooks on advanced mechanics, however, this present text eschews a primarily technical and formalistic treatment in favor of a fundamental, historical, philosophical approach. As the author remarks, there is a tremendous treasure of philosophical meaning" behind t…
Read More ↓Title Statements
- Full title :The Variational Principles of Mechanics.
Summary
Analytical mechanics is, of course, a topic of perennial interest and usefulness in physics and engineering, a discipline that boasts not only many practical applications, but much inherent mathematical beauty. Unlike many standard textbooks on advanced mechanics, however, this present text eschews a primarily technical and formalistic treatment in favor of a fundamental, historical, philosophical approach. As the author remarks, there is a tremendous treasure of philosophical meaning" behind the great theories of Euler and Lagrange, Hamilton, Jacobi, and other mathematical thinkers. Well-written, authoritative, and scholarly, this classic treatise begins with an introduction to the variational principles of mechanics including the procedures of Euler, Lagrange, and Hamilton. Ideal for a two-semester graduate course, the book includes a variety of problems, carefully chosen to familiarize the student with new concepts and to illuminate the general principles involved. Moreover, it offers excellent grounding for the student of mathematics, engineering, or physics who does not intend to specialize in mechanics, but wants a thorough grasp of the underlying principles. The late Professor Lanczos (Dublin Institute of Advanced Studies) was a well-known physicist and educator who brought a superb pedagogical sense and profound grasp of the principles of mechanics to this work, now available for the first time in an inexpensive Dover paperback edition. His book will be welcomed by students, physicists, engineers, mathematicians, and anyone interested in a clear masterly exposition of this all-important discipline
Read More ↓Edition Statements
- Publication Date:2012.
Publication Statements
- Publisher(s):Dover Publications
- Language:eng
- Publication Date:2012.
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:9780486134703, 0486134709
- oclc:ocn969061058
- LC Classification:QA805 .L278 2012
- Dewey Decimal:531/.01/51
Table of Contents
Cover Page; Title Page; Copyright Page; Dedication; Preface; Preface to the Second Edition; Preface to the Second Edition; Preface to the Second Edition; Contents; Introduction; 1. The variational approach to mechanics; 2. The procedure of Euler and Lagrange; 3. Hamilton's procedure; 4. The calculus of variations; 5. Comparison between the vectorial and the variational treatments of mechanics; 6. Mathematical evaluation of the variational principles; 7. Philosophical evaluation of the variational approachto mechanics; The Variational Principles of Mechanics.
I. The Basic Concepts of Analytical Mechanics1. The principal view points of analytical mechanics; 2. Generalized coordinates; 3. The configuration space; 4. Mapping of the space on itself; 5. Kinetic energy and Riemannian geometry; 6. Holonomic and non-holonomic mechanical systems; 7. Work function and generalized force; 8. Scleronomic and rheonomic systems. The law of theconservation of energy; 1. The general nature of extremum problems; 2. The stationary value of a function; 3. The second variation; 4. Stationary value versus extremum value; 5. Auxiliary conditions. The Lagrangian n-method.
6. Non-holonomic auxiliary cond…
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