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Lagrange’s identity and its generalizations. (English) Zbl 1229.82090
Summary: 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.

MSC:
82B30 Statistical thermodynamics
37A60 Dynamical aspects of statistical mechanics
70H03 Lagrange’s equations
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