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Izvestiya Vysshikh Uchebnykh Zavedenii Matematika
Article . 2009
Data sources: CyberLeninka - Russian open access scientific library
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Одномерные лагранжианы, порожденные квадратичной формой

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2009 Russian Publisher:Федеральное государственное автономное образовательное учреждение высшего образования «Казанский (Приволжский) федеральный университет»Journal:Известия высших учебных заведений. Математика (issn: 0021-3446, eissn: 2076-4626, Copyright policy )

Одномерные лагранжианы, порожденные квадратичной формой

Abstract

В данной статье классическое вариационное исчисление применяется к лагранжианам специального вида: даются формулы для первых интегралов, указывается способ получения инвариантных первых интегралов, выводятся дифференциальные условия однородности лагранжианов относительно умножения пути х (t) на функцию с (t) и относительно замены параметра t = t (s).

Keywords

CONFORMALLY CONNECTED MANIFOLD,УРАВНЕНИЕ ЭЙЛЕРА-ЛАГРАНЖА,EULER-LAGRANGE EQUATION,ИНТЕГРАЛЬНЫЕ ФУНКЦИОНАЛЫ,INTEGRAL FUNCTIONALS,ИЗОТРОПНАЯ ЭКСТРЕМАЛЬНАЯ КРИВАЯ,ISOTROPIC EXTREME CURVE,ОДНОМЕРНЫЕ ЛАГРАНЖИАНЫ,ONE-DIMENSIONAL LAGRANGIANS,ОРТОГОНАЛЬНАЯ ГРУППА,ORTHOGONAL GROUP,ПУТЬ,PATH,КВАДРАТИЧНАЯ ФОРМА,QUADRATIC FORM,СКАЛЯРНОЕ ПРОИЗВЕДЕНИЕ,SCALAR PRODUCT,МНОГООБРАЗИЕ КОНФОРМНОЙ СВЯЗНОСТИ

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
bronze