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Regular and Chaotic Dynamics, 2008, Volume 13, Issue 2, Pages 71–80
DOI: https://doi.org/10.1134/S1560354708020019 (Mi rcd561) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Lagrange’s Identity and Its Generalizations

V. V. Kozlov

V.A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Citations (2)
DOI: https://doi.org/10.1134/S1560354708020019
Abstract: The famous Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through the kinetic energy and homogeneous potential energy. The paper presents various extensions of this brilliant result to the case 1) of constrained mechanical systems, 2) when the potential energy is quasi-homogeneous in coordinates and 3) of continuum of interacting particles governed by the well-known Vlasov kinetic equation.
Keywords: Lagrange’s identity, quasi-homogeneous function, dilations, Vlasov’s equation.
Received: 14.01.2008
Accepted: 07.02.2008
Bibliographic databases:
Document Type: Article
MSC: 37A60, 82B30, 82CXX
Language: English
Citation: V. V. Kozlov, “Lagrange’s Identity and Its Generalizations”, Regul. Chaotic Dyn., 13:2 (2008), 71–80
Citation in format AMSBIB
\Bibitem{Koz08}
\by V.~V.~Kozlov
\paper Lagrange’s Identity and Its Generalizations
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 2
\pages 71--80
\mathnet{http://mi.mathnet.ru/rcd561}
\crossref{https://doi.org/10.1134/S1560354708020019}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2395526}
\zmath{https://zbmath.org/?q=an:1229.82090}
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  • https://www.mathnet.ru/eng/rcd561
  • https://www.mathnet.ru/eng/rcd/v13/i2/p71
    • This publication is cited in the following 2 articles:
    1. A. A. Kilin, “Chislennoe modelirovanie mnogochastichnykh sistem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2009, no. 3, 135–146  mathnet
    2. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Multiparticle Systems. The Algebra of Integrals and Integrable Cases”, Regul. Chaotic Dyn., 14:1 (2009), 18–41  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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