Perfect Form (eBook)

Variational Principles, Methods, and Applications in Elementary Physics

Don S. Lemons (Autor)

eBook Download: PDF

2020
136 Seiten
Princeton University Press (Verlag)
978-0-691-21482-5 (ISBN)

Infos

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 "e;perfect form"e; 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 "e;variational"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 7.7.2020
• Zusatzinfo: 39 line illus.
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Plasmaphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Schlagworte: Action (physics) • Angular displacement • Aristotelean causes • Aristotelian physics • Aristotle • Axiom • Bernoulli, Johann • Blaise Pascal • Boundary value problem • Brachistochrone • Calculus of Variations • cantilever model • Cartesian coordinate system • Catenary • Center of mass (relativistic) • classical mechanics • Conservation of Energy • Conserved quantity • coordinate system • Curvature • Cylinder (geometry) • D'alembert's Principle • Derivative • Descartes, Rene • Diagram (category theory) • Differentiable function • differential equation • Diffusion Equation • E0 • effective potential • efficient cause • Electric potential energy • energy conservation • Equation • Equations of motion • Ernst Mach • Euler–Lagrange equation • Fermat's Principle • Figure of the Earth • final cause • First principle • focal length • Free particle • Gauss's Law • Generalized coordinates • geometrical optics • Gravity • Hamiltonian System • Hamilton–Jacobi equation • Hamilton's principle • harmonic motion • Hermann Bondi • holonomic constraints • Hooke's law • horizontal plane • Hyperbola • ignorable coordinate • Incompressible Flow • inflection point • Initial Value Problem • isopermetric constraints • Jacobi, C.G J. • Kepler's Third Law • Lagrange multiplier • Lagrange multipliers • Lagrangian • Lagrangian (field theory) • Lagrangian mechanics • least resistance • Leonhard Euler • Ludwig Boltzmann • Massive particle • Mathematical Optimization • Mathematical problem • Mathematics • Maxima and minima • mechanical equilibrium • Mechanics • meridional rays • mirages • Modern Physics • Moment of Inertia • multiple Integral • Natural Boundary Conditions • Net force • Newtonian dynamics • Newton's law of universal gravitation • Newton's laws of motion • Optical Path Length • orbit shapes • ordinary differential equation • Parabola • Parabolic trajectory • Parameter • partial differential equation • Pascal's law • Photon • Poisson's Equation • polynomial • potential energy • potential function • principia • principle of least action • Principle of Relativity • projectile trajectory • Proportionality (mathematics) • Quantity • Quantum Gravity • Ray (optics) • refraction • Refractive index • Richard Feynman • Rotational Symmetry • Schrödinger equation • slinky • Snell's law • Special case • Special relativity • specular reflection • spherical pendulum • stationary process • theoretical physics • Time evolution • Total derivative • true rays • Variable (mathematics) • Variational method (quantum mechanics) • Variational Principle • wave function
• ISBN-10: 0-691-21482-4 / 0691214824
• ISBN-13: 978-0-691-21482-5 / 9780691214825