On the axiomatic foundations of dimensional analysis
Gawain, Theodore Henry
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This paper reformulates the basic axioms of dimensional analysis so as to clear up some deeply entrenched misconceptions relating to the nature of physical dimensions and generalized units. Certain novel relations are thereby discovered which although unorthodox are nevertheless useful and correct. It is shown how various systems or natural units can be constructed so as to embody the same logical structure that characterizes some given system of fixed units. The important fact is brought out that every physical equation which is valid in some given system of units remains valid if all quantities be converted into any other system which embodies the same logical structure. The paper also show that the dimensionless pi's of Buckingham's Pi Theorem simply represent various physical parameters as expressed in some appropriate system of consistent natural units. The fundamental dimensional principles considered in this paper apply in some form to every quantitative analytical and experimental problem in the entire realm of physical science and engineering. (Author)
NPS Report NumberNPS-57G1171+051
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