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Perfect Form: Variational Principles, Methods, and Applications in Elementary Physics

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Publisher Comments:

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.

Synopsis:

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.

About the Author

Don S. Lemons is Associate Professor of Physics at Bethel College of North Newton, Kansas.

Table of Contents

Preface
Ch. 1Least Time3
Ch. 2Calculus of Variations17
Ch. 3Curved Light33
Ch. 4Least Potential Energy45
Ch. 5Least Action69
Ch. 6Hamilton's Principle - Restricted81
Ch. 7Hamilton's Principle - Extended95
Index115

Product Details

ISBN:
9780691026633
Subtitle:
Variational Principles, Methods, and Applications in Elementary Physics
Author:
Lemons, Don S.
Publisher:
Princeton University Press
Location:
Princeton, N.J. :
Subject:
Physics
Subject:
Mathematical Physics
Subject:
Calculus of variations
Subject:
Physics and Astroscience
Subject:
Physics-Math
Copyright:
Edition Description:
Trade paper
Series Volume:
no. 29
Publication Date:
March 1997
Binding:
Paperback
Grade Level:
College/higher education:
Language:
English
Illustrations:
39 line illus.
Pages:
136
Dimensions:
9 x 6 in 9 oz

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Related Subjects

History and Social Science » Military » General History
Science and Mathematics » Physics » Classical Mechanics
Science and Mathematics » Physics » General
Science and Mathematics » Physics » General History and Philosophy
Science and Mathematics » Physics » Math

Perfect Form: Variational Principles, Methods, and Applications in Elementary Physics New Trade Paper
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Product details 136 pages Princeton University Press - English 9780691026633 Reviews:
"Synopsis" by , 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.

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