Some matrix aspects of generalized dimensional analysis

Summary Recent group theoretic techniques effective for reducing the number of variables in systems of partial differential equations are invoked to formulate a generalized approach to dimensional analysis. It is then shown that significant conclusions can be elicited upon consideration of adimensional matrix arising via the group formulation. In particular, a generalized form of Sedov's self-similarity criterion is shown to exist within the framework of the approach developed. The presentation is concluded by consideration of three illustrations.This research has been sponsored in part by the Mathematics Research Center, United States Army, The University of Wisconsin, under Contract No. DA-31-124-AR0-D-462. The paper is based upon a presentation made at the Sixteenth Conference of Army Mathematicians, Bethesda, Maryland, May, 1970.