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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, Issue 3, Pages 69–74 (Mi vuu128)

MECHANICS

Generalization of Lagrange's identity and new integrals of motion

A. A. Kilin

Udmurt State University

Abstract: We discuss system of material points in Euclidean space interacting both with each other and with external field. In particular we consider systems of particles whose interacting is described by homogeneous potential of degree of homogeneity $\alpha=-2$. Such systems were first considered by Newton and – more systematically – by Jacobi). For such systems there is an extra hidden symmetry, and corresponding first integral of motion which we call Jacobi integral. This integral was given in different papers starting with Jacobi, but we present in general. Furthermore, we construct a new algebra of integrals including Jacobi integral. A series of generalizations of Lagrange's identity for systems with homogeneous potential of degree of homogeneity $\alpha=-2$ is given. New integrals of motion for these generalizations are found.

Keywords: Lagrange's identity, many-particle system, first integral, integrability, algebra of integrals.

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Document Type: Article
UDC: 531.011
MSC: 70F, 37E

Citation: A. A. Kilin, “Generalization of Lagrange's identity and new integrals of motion”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 3, 69–74

Citation in format AMSBIB
\Bibitem{Kil08} \by A.~A.~Kilin \paper Generalization of Lagrange's identity and new integrals of motion \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2008 \issue 3 \pages 69--74 \mathnet{http://mi.mathnet.ru/vuu128}