Details

Autor(en) / Beteiligte

• Bobylev, N. A
• Emel’yanov, S. V
• Korovin, S. K

Titel

Geometrical Methods in Variational Problems [Elektronische Ressource]

Ist Teil von

• Mathematics and Its Applications : 485

Ort / Verlag

Dordrecht : Springer Netherlands

Erscheinungsjahr

1999

Link zum Volltext

• Volltext

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• Since the building of all the Universe is perfect and is created by the wisdom Creator, nothing arises in the Universe in which one cannot see the sense of some maXImum or mInImUm Euler God moves the Universe along geometrical lines Plato Mathematical models of most closed physical systems are based on variational principles, i.e., it is postulated that equations describing the evolution of a system are the Euler~Lagrange equations of a certain functional. In this connection, variational methods are one of the basic tools for studying many problems of natural sciences. The first problems related to the search for extrema appeared as far back as in ancient mathematics. They go back to Archimedes, Appolonius, and Euclid. In many respects, the problems of seeking maxima and minima have stimulated the creation of differential calculus; the variational principles of optics and mechanics, which were discovered in the seventeenth and eighteenth centuries, gave impetus to an intensive development of the calculus of variations. In one way or another, variational problems were of interest to such giants of natural sciences as Fermat, Newton, Descartes, Euler, Huygens, 1. Bernoulli, J. Bernoulli, Legendre, Jacobi, Kepler, Lagrange, and Weierstrass