Lagrange’s Identity and Its Generalizations

    2008, Volume 13, Number 2, pp.  71-80

    Author(s): Kozlov V. V.

    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
    Citation: Kozlov V. V., Lagrange’s Identity and Its Generalizations, Regular and Chaotic Dynamics, 2008, Volume 13, Number 2, pp. 71-80

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