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

摘要

A transformation, originally due to Staniukovich, which transforms a differential equation for p(h,t) in a homentropic flow, into a differential equation for p1(h1,t) in a flow of an LMS-gas is applied to the general theory. It yields transformation rules for all the flow parameters. Next the Staniukovich transformation is generalized resulting in a 3 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.