# Geometrical Methods in Variational Problems

## byN.A. Bobylov, S.V. Emel'yanov, S. Korovin

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Since the building of all the Universe is perfect and is cre­ ated 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 vari­ ational principles, i.e., it is postulated that equations describing the evolu­ tion of a system are the Euler<_lagrange20_equations20_of20_a20_certain20_functional.20_in20_this20_connection2c_20_variational20_methods20_are20_one20_of20_the20_basic20_tools20_for20_studying20_many20_problems20_of20_natural20_sciences.20_the20_first20_problems20_related20_to20_the20_search20_for20_extrema20_appeared20_as20_far20_back20_as20_in20_ancient20_mathematics.20_they20_go20_back20_to20_archimedes2c_20_appolonius2c_20_and20_euclid.20_in20_many20_respects2c_20_the20_problems20_of20_seeking20_maxima20_and20_minima20_have20_stimulated20_the20_creation20_of20_differential20_calculus3b_20_the20_variational20_princ2ad_20_ciples20_of20_optics20_and20_mechanics2c_20_which20_were20_discovered20_in20_the20_seventeenth20_and20_eighteenth20_centuries2c_20_gave20_impetus20_to20_an20_intensive20_development20_of20_the20_calculus20_of20_variations.20_in20_one20_way20_or20_another2c_20_variational20_problems20_were20_of20_interest20_to20_such20_giants20_of20_natural20_sciences20_as20_fermat2c_20_newton2c_20_descartes2c_20_euler2c_20_huygens2c_20_1.20_bernoulli2c_20_j.20_bernoulli2c_20_legendre2c_20_jacobi2c_20_kepler2c_20_lac2ad_20_grange2c_20_and20_weierstrass. equations="" of="" a="" certain="" functional.="" in="" this="" _connection2c_="" variational="" methods="" are="" one="" the="" basic="" tools="" for="" studying="" many="" problems="" natural="" sciences.="" first="" related="" to="" search="" extrema="" appeared="" as="" far="" back="" ancient="" mathematics.="" they="" go="" _archimedes2c_="" _appolonius2c_="" and="" euclid.="" _respects2c_="" seeking="" maxima="" minima="" have="" stimulated="" creation="" differential="" _calculus3b_="" _princ2ad_="" ciples="" optics="" _mechanics2c_="" which="" were="" discovered="" seventeenth="" eighteenth="" _centuries2c_="" gave="" impetus="" an="" intensive="" development="" calculus="" variations.="" way="" or="" _another2c_="" interest="" such="" giants="" sciences="" _fermat2c_="" _newton2c_="" _descartes2c_="" _euler2c_="" _huygens2c_="" 1.="" _bernoulli2c_="" j.="" _legendre2c_="" _jacobi2c_="" _kepler2c_="" _lac2ad_="" _grange2c_="">
Title:Geometrical Methods in Variational ProblemsFormat:PaperbackDimensions:543 pagesPublished:October 13, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401059551

ISBN - 13:9789401059558