| Description |
1 online resource (xi, 117 p.) |
| Contents |
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 |
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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 |
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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 |
| Summary |
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 |
| Analysis |
Aristotelean causes |
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Aristotle |
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Bernoulli, Johann |
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Descartes, Rene |
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Jacobi, C.G J |
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Kepler's Third Law |
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Lagrange multipliers |
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Lagrangian |
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Principia |
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brachistochrone |
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calculus of variations |
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cantilever model |
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effective potential |
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efficient cause |
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final cause |
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focal length |
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generalized coordinates |
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geometrical optics |
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harmonic motion |
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holonomic constraints |
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ignorable coordinate |
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isopermetric constraints |
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least resistance |
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meridional rays |
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mirages |
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natural boundary conditions |
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optical path length |
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orbit shapes |
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projectile trajectory |
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spherical pendulum |
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true rays |
| Notes |
Includes index |
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Description based on print version record and CIP data provided by publisher; resource not viewed |
| Subject |
Calculus of variations.
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Mathematical physics.
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SCIENCE / Physics / General
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Mathematical physics.
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Calculus of variations.
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| Form |
Electronic book
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| LC no. |
2021698795 |
| ISBN |
9780691214825 |
|
0691214824 |
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9780691026640 |
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0691026645 |
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9780691026633 |
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0691026637 |
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