Perfect Form

by Don S. Lemons

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.

Genres: Physics

130 pages, Hardcover

First published March 1, 1997

Reviews

[Mohamed · Rating 4 out of 5]

I just took an independent study in the calculus of variations , This is an engaging book, written on a fairly basic level. Any junior with some calculus should be able to handle it. The author has done a great job of introducing the calculus of variations, Lagrange multipliers, etc, and applying them to clear examples from physics (Fermat's principle, Lagrangians and Hamiltonians).

[dead letter office · Rating 4 out of 5]

A favorite of mine. I ran into Lemons on the streets of Los Alamos. He seemed happy to see me, despite having no apparent idea who I was. You have to like the people who are happy to see strangers again.