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Dimensional Analysis in Computer Algebra

Raya Khanin
Organization: University of Cambridge
Department: Department of Applied Mathematics and Theoretical Physics
Journal / Anthology

International Conference on Symbolic and Algebraic Computation
Year: 2001
Volume: ISSAC '01
Page range: 201-208

The goal of this paper is to demonstrate the introduction of dimensional variables as well as the applications of dimensional analysis in Computer Algebra system (Mathematica). The package DimensionalAnalysis developed by author uses nondimensionalization based on II-theorem to simplify equations and to reduce the number of parameters when the governing equations are not known. The package contains symbols, dimensional formulae and units for principal physical quantities, as well as a number of named dimensionless parameters. Another important feature of the package is its ability to check the dimensional homogeneity of the expressions. This package is aimed at helping researchers with the preliminary analysis of models and simplification of large-scale problems by using dimensionless parameters. The package can also be used in teaching.

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dimensional variables, dimensional analysis, nondimensionalization, Computer Algebra