Lagrange’s identity and its generalizations
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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.
Key wordsLagrange’s identity quasi-homogeneous function dilations Vlasov’s equation
MSC2000 numbers37A60 82B30 82CXX
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