Cargando…
The Principle of Least Action : History and Physics.
This text brings history and the key fields of physics together to present a unique technical discussion of the principles of least action.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2018.
©2018 |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title page; Title page; Copyright page; Contents; List of illustrations; Acknowledgments; 1 Introduction; 2 Prehistory of Variational Principles; 2.1 Queen Dido and the Isoperimetric Problem; 2.1.1 Zenodorus's Solution*; 2.2 Hero of Alexandria and the Law of Reflection; 2.3 Galileo and the Curve of Swiftest Descent; 2.4 Bending of Light Rays and Fermat's Minimum Principle; 2.4.1 Fermat's Method of Maxima and Minima; 2.4.2 Huygens' Simplified Derivation of Snell's Law; 2.5 Newton and the Solid of Least Resistance*; 2.5.1 The Sphere and the Cylinder.
- 2.5.2 An Application "in the Building of Ships"2.5.3 The First Genuine Variational Calculation; 3 An Excursion to Newton's Principia; 3.1 Newton's Propositions on the Laws of Motion; 3.2 Geometrical Derivation of Kepler's Laws of Planetary Motion; 3.2.1 Proposition 1: Equal Areas are Swept Out in Equal Times; 3.2.2 Proposition 6: The Force Law and the Geometry of the Orbit*; 3.2.3 Circular Orbits; 3.2.4 Proposition 10: Elliptical Orbit with the Center of Force at the Center of the Ellipse; 3.2.5 Proposition 11: Center of Force at the Focus of the Ellipse*
- 4 The Optical-Mechanical Analogy, Part I4.1 Bernoulli's Challenge and the Brachistochrone; 4.1.1 Huygens and the Horologium Oscillatorium; 4.1.2 Leibniz's Solution of the Brachistochrone; 4.1.3 Bernoulli's Solution: Particle Paths as Light Rays; 4.2 Maupertuis, Least Action, and Metaphysical Mechanics; 4.3 Euler and the Method of Maxima and Minima*; 4.3.1 Euler's Derivation of Orbits from the Least Action Principle; 4.4 Examples of the Optical-Mechanical Analogy; 4.4.1 Conservation of "Angular Momentum" for Light Rays; 4.4.2 The Terrestrial Brachistochrone.
- 4.5 The String Analogy and the Principle of Least Action4.5.1 The Least Action Principle and Stretchable Strings; 5 D'Alembert, Lagrange, and the Statics-Dynamics Analogy; 5.1 The Principle of Virtual Work; 5.2 Statics Meets Dynamics: Bernoulli's Calculation of the Center of Oscillation; 5.3 D'Alembert's Principle; 5.4 Lagrange's Dynamics; 5.4.1 Lagrange's "Scientific Poem"; 5.4.2 Symmetries; 5.5 Lagrange versus d'Alembert: Dissipative and Nonholonomic Systems; 5.5.1 Dissipation in a Reversible System: Lamb's Model; 5.5.2 Nonholonomic Systems; 5.6 Gauss's Principle of Least Constraint.
- 5.7 Least Action with a Twist: the Elasticity of the Ether and Maxwell's Equations*6 The Optical-Mechanical Analogy, Part II: The Hamilton-Jacobi Equation; 6.1 Hamilton's "Theory of Systems of Rays"; 6.2 Conical Refraction*; 6.2.1 Fresnel's Equations for Anisotropic Crystals; 6.2.2 Analytical Derivation of the Wave Surface; 6.2.3 Hamilton's Derivation of the Conical Cusp; 6.2.4 Internal Conical Refraction: "The Plum Laid Down on a Table"; 6.3 Hamilton's Law of Varying Action*; 6.4 An Example from Hamilton: The Characteristic Function V for a Parabolic Orbit*