A01=Don S. Lemons
Action (physics)
Angular displacement
Aristotelian physics
Author_Don S. Lemons
Axiom
Boundary value problem
Cartesian coordinate system
Category=PHD
Catenary
Classical mechanics
Conserved quantity
Coordinate system
D'Alembert's principle
Derivative
Differential equation
E0
Energy conservation
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eq_nobargain
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Equation
Equations of motion
Euler-Lagrange equation
Fermat's principle
Free particle
Gauss's law
Geometrical optics
Hamilton's principle
Hermann Bondi
Hooke's law
Horizontal plane
Hyperbola
Incompressible flow
Inflection point
Initial value problem
Lagrange multiplier
Lagrangian (field theory)
Lagrangian mechanics
Leonhard Euler
Massive particle
Mathematical optimization
Maxima and minima
Mechanical equilibrium
Mechanics
Modern physics
Net force
Newton's law of universal gravitation
Newton's laws of motion
Ordinary differential equation
Parabola
Parabolic trajectory
Parameter
Partial differential equation
Pascal's law
Photon
Poisson's equation
Potential energy
Potential function
Principle of least action
Quantity
Quantum gravity
Ray (optics)
Refraction
Refractive index
Rotational symmetry
Schrodinger equation
Snell's law
Special case
Special relativity
Stationary process
Time evolution
Total derivative
Variable (mathematics)
Variational method (quantum mechanics)
Variational principle
Product details
- ISBN 9780691026633
- Weight: 170g
- Dimensions: 152 x 235mm
- Publication Date: 23 Mar 1997
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Don S. Lemons is Associate Professor of Physics at Bethel College of North Newton, Kansas.
