Notes on the Unsteady Rectilinear Motion of a Perfect Gas. Part 6: On a Transformation of Staniukovich and Its Generalization

摘要

A transformation which transforms a differential equation for p(h, t) in a homentropic flow into a differential equation for p sub 1 (h sub 1, t) in a flow of a Ludford-Martin-Staniukovich gas is applied to the general theory of transformations of the equations of motion for the unsteady rectilinear flow of a perfect gas. The Staniukovich transformation is generalized, resulting in a three parameter continuous transformation group. The infinitesimal operators of the group are obtained and the invariance of a number of differential equations under the transformation is established.