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.
This publication is cited in the following 2 articles:
A. A. Kilin, “Chislennoe modelirovanie mnogochastichnykh sistem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2009, no. 3, 135–146
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