Geodesic
Lagrange's identity and its generalizations
Russian journal of nonlinear dynamics, Tome 4 (2008) no. 2, pp. 157-168

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : dilations, Vlasov's equation. 
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     author = {V. V. Kozlov},
     title = {Lagrange's identity and its generalizations},
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V. V. Kozlov. Lagrange's identity and its generalizations. Russian journal of nonlinear dynamics, Tome 4 (2008) no. 2, pp. 157-168. http://geodesic.mathdoc.fr/item/ND_2008_4_2_a3/