Perfect form : variational principles, methods, and applications in elementary physics /

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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lemons, Don S. (Don Stephen), 1949-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 1997.
Temas:
Calculus of variations.
Mathematical physics.
Calcul des variations.
Physique mathématique.
SCIENCE / Physics / General
Mathematical physics
Calculus of variations
Aristotelean causes.
Aristotle.
Bernoulli, Johann.
Descartes, Rene.
Jacobi, C.G J.
Kepler's Third Law.
Lagrange multipliers.
Lagrangian.
Principia.
brachistochrone.
calculus of variations.
cantilever model.
effective potential.
efficient cause.
final cause.
focal length.
generalized coordinates.
geometrical optics.
harmonic motion.
holonomic constraints.
ignorable coordinate.
isopermetric constraints.
least resistance.
meridional rays.
mirages.
natural boundary conditions.
optical path length.
orbit shapes.
projectile trajectory.
spherical pendulum.
true rays.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover Page
  • Half-title Page
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • Chapter One: Least Time
  • 1.1 Important Facts
  • 1.2 An Interpretation
  • 1.3 Fermat's Principle
  • 1.4 Image Formation
  • 1.5 Final Cause
  • Chapter Two: Calculus of Variations
  • 2.1 An Introductory Problem
  • 2.2 Euler-Lagrange Equation
  • 2.3 First Integrals
  • 2.4 More Than One Unknown Function
  • Chapter Three: Curved Light
  • 3.1 Planar Atmosphere
  • 3.2 Road Surface Mirage
  • 3.3 Fiberoptic
  • 3.4 Parametric Ray Equations
  • Chapter Four: Least Potential Energy
  • 4.1 Principle Of Least Potential Energy
  • 4.2 Elementary Examples
  • 4.3 Constraints
  • 4.4 Lagrange Multipliers
  • 4.5 Catenary
  • 4.6 Natural Boundary Conditions
  • 4.7 Vertically Hanging Elastic Column
  • Chapter Five: Least Action
  • 5.1 Maupertuis
  • 5.2 Jacobfs Principle Of Least Action
  • 5.3 Projectile Trajectory
  • 5.4 Optics And Mechanics
  • Chapter Six: Hamilton's Principle-Restricted
  • 6.1 Hamilton's Principle
  • 6.2 Deriving The Restricted Hamilton's Principle
  • 6.3 Spherical Pendulum
  • 6.4 Lagrange And Hamilton
  • Chapter Seven: Hamilton's Principle-Extended
  • 7.1 Hamiltonian Systems
  • 7.2 Watt's Governor
  • 7.3 Multiparticle Systems
  • 7.4 Two-Body Central Potential
  • 7.5 Generalized Coordinates
  • 7.6 Sliding Ladder
  • 7.7 Summary And Prospect
  • Index

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