A General Similarity Theory of Partial Differential Equations and its Use in the Solution of Problems in Aeronautics

[摘要] A general similarity theory of systems of partial differential equations of any order in any number of independent variables is developed with the aid of the theory of continuous one-parameter groups of transformations. The theory is illustrated by means of several known examples of similarity equations, previously given without motivation, in Hydrodynamics. With the aid of the theory two new examples of similarity equations, one in Elasticity and one in Fluid Mechanics, have been found; these are discussed in the text.

[发布机构] University:California Institute of Technology;Department:Engineering and Applied Science

[关键词] Aeronautics and Mathematics