Invariant Variational Principles [antikvár]

Preface This monograph deals almost exclusively with calculus of variations problems that are invariant under an r-parameter family of transformations. Since the early part of this century when Emmy Noether wrote her monumental paper on the subject, invariant variational principles have attained extensive application to a wide range of problems in physics and engineering; indeed, the Noether theorem has become one of the basic building blocks of modern field theories. The goal of this monograph is to transmit the flavor of some of these problems and applications and to present some concrete examples which it is hoped will lead the reader to appreciate the connection between invariance transformations and conservation laws for physical systems. This monograph grew out of courses and seminars that the author conducted at the Ohio State University, the University of Dayton, the University of Arizona, and at Kansas State University over the past six years. Motivated by the belief that invariance problems do not get the attention they deserve in elementary courses in the calculus of variations, the author has injected much of this material in a standard course on the subject as a supplement to a basic textbook. The material has also been offered in a one-semester three-hour special topics course in applied mathematics. The audience has generally been upper division undergraduate students or graduate students in mathematics, physics, or applied science. The book is more or less self-contained and the prerequisites are minimal—undergraduate physics and standard courses in advanced calculus and linear