Poincaré’s formalism is used to develop a variant of the usual virialtheorem in which the time average of the equation of motion of a certain function isexpressed in terms of the generalized Poisson brackets.
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Generalisation of the Hamilton-Jacobi theorem[J] . Q. K. Ghori,M. Hussain.Zeitschrift für angewandte Mathematik und Physik ZAMP . 1974 (4)