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 powerful ones through generalization One selection of text and problems even constitutes a non calculus of variations introduction to variational methods, while the mathematics 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....
|Publisher||:||Princeton University Press March 3, 1997|
|Number of Pages||:||136 pages|
|File Size||:||886 KB|
|Status||:||Available For Download|
|Last checked||:||21 Minutes ago!|
Perfect Form Reviews
I just took an independent study in the calculus of variations out of Gelfand's classic text. I covered the first four chapters which is a nice introduction. However the text is pretty technical and so Perfect Form (PF) was a great companion. Its laid back, accessible to a sophomore physics student and fine for self study. It has a range of physical problems from calculations to nice little problems to think about.
this is a poor effort even for a sketchy introduction --
For a third or fourth year student in physics this short book, Perfect Form, would be near perfect as either a short overview of variational methods, or as a supplementary text for an advanced classical physics course.
I don't understand Mr. Lemons. It seems that he has assigned himself the task of writing watered down, dispensable versions of books that have already been written on the same subjects and for the same audience. Let me be more specific:
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). I only wish he had expanded the topics somewhat to introduce a few more topics to whet the appetite, such as phase spaces, Liouville's theorem, Noether's theorem.