Publication:
On the axiomatic foundations of dimensional analysis

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Authors
Gawain, Theodore Henry
Subjects
Dimensional Analysis, Generalized Units, Pi Theorem, Mathematical Invariance of Physical Equations, Consistent Units, Natural Units
Advisors
Date of Issue
1974-05
Date
1974-05
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
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)
Type
Technical Report
Description
Series/Report No
Department
Aeronautics
Identifiers
NPS Report Number
NPS-57G1171+051
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Funder
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
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