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

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

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
VerfasserIn:
Lemons, Don S.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2021]
©1997
Year of Publication:2021
Language:English
Online Access:
Physical Description:1 online resource (136 p.) :; 39 line illus.
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100 1 |a Lemons, Don S.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Perfect Form :  |b Variational Principles, Methods, and Applications in Elementary Physics /  |c Don S. Lemons. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2021] 
264 4 |c ©1997 
300 |a 1 online resource (136 p.) :  |b 39 line illus. 
336 |a text  |b txt  |2 rdacontent 
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505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t CHAPTER ONE. Least Time --   |t CHAPTER TWO. Calculus of Variations --   |t CHAPTER THREE. Curved Light --   |t CHAPTER FOUR. Least Potential Energy --   |t CHAPTER FIVE. Least Action --   |t CHAPTER SIX. Hamilton's Principle-Restricted --   |t CHAPTER SEVEN. Hamilton's Principle-Extended --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) 
650 0 |a Calculus of variations. 
650 0 |a Mathematical physics. 
650 7 |a SCIENCE / Physics / General.  |2 bisacsh 
653 |a Aristotelean causes. 
653 |a Aristotle. 
653 |a Bernoulli, Johann. 
653 |a Descartes, Rene. 
653 |a Jacobi, C.G J. 
653 |a Kepler's Third Law. 
653 |a Lagrange multipliers. 
653 |a Lagrangian. 
653 |a Principia. 
653 |a brachistochrone. 
653 |a calculus of variations. 
653 |a cantilever model. 
653 |a effective potential. 
653 |a efficient cause. 
653 |a final cause. 
653 |a focal length. 
653 |a generalized coordinates. 
653 |a geometrical optics. 
653 |a harmonic motion. 
653 |a holonomic constraints. 
653 |a ignorable coordinate. 
653 |a isopermetric constraints. 
653 |a least resistance. 
653 |a meridional rays. 
653 |a mirages. 
653 |a natural boundary conditions. 
653 |a optical path length. 
653 |a orbit shapes. 
653 |a projectile trajectory. 
653 |a spherical pendulum. 
653 |a true rays. 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Archive 1927-1999  |z 9783110442496 
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