Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon’s data plot then specify a unique differential equation for it

摘要

BackgroundThis study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot’s mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon.