Perfect form : variational principles, methods, and applications in elementary physics / Don S. Lemons.

Format:

Book

Author/Creator:

Lemons, Don S. (Don Stephen), 1949- author.

Language:

English

Subjects (All):

Calculus of variations.

Mathematical physics.

Physical Description:

1 online resource (xi, 117 pages) : illustrations

Place of Publication:

Princeton, New Jersey : Princeton University Press, [1997]

Summary:

What does the path taken by a ray of light share with the trajectory of a thrown baseball and the curve of a wheat stalk bending in the breeze? Each is the subject of a different study yet all are optimal shapes; light rays minimize travel time while a thrown baseball minimizes action. All natural curves and shapes, and many artificial ones, manifest such "perfect form" because physical principles can be expressed as a statement requiring some important physical quantity to be mathematically maximum, minimum, or stationary. Perfect Form introduces the basic "variational" principles of classical physics (least time, least potential energy, least action, and Hamilton's principle), develops the mathematical language most suited to their application (the calculus of variations), and presents applications from the physics usually encountered in introductory course sequences. The text gradually unfolds the physics and mathematics. While other treatments postulate Hamilton's principle and deduce all results from it, Perfect Form begins with the most plausible and restricted variational principles and develops more powerful ones through generalization. One selection of text and problems even constitutes a non-calculus of variations introduction to variational methods, while the mathematics more generally employed extends only to solving simple ordinary differential equations. Perfect Form is designed to supplement existing classical mechanics texts and to present variational principles and methods to students who approach the subject for the first time.

Contents:

Frontmatter

Contents

Preface

CHAPTER ONE. Least Time

CHAPTER TWO. Calculus of Variations

CHAPTER THREE. Curved Light

CHAPTER FOUR. Least Potential Energy

CHAPTER FIVE. Least Action

CHAPTER SIX. Hamilton's Principle—Restricted

CHAPTER SEVEN. Hamilton's Principle—Extended

Index

Notes:

Description based on print version record.

Includes index.

ISBN:

9780691214825

0691214824