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- W4308671844 abstract "We present an innovative approach to dimensional analysis, based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem, grounded in a purely algebraic theory of quantity spaces, allows the traditional $pi$ theorem to be restated in an explicit and precise form and its prerequisites to be the clarified and relaxed. Examples of dimensional analysis based on the new approach are given, showing that results obtained by traditional dimensional analysis can be strengthened. For example, the orbital period of a two-body system can be derived without use of equations of motion. The connection between dimensional analysis and matroid theory is also explored." @default.
- W4308671844 created "2022-11-14" @default.
- W4308671844 creator A5050166551 @default.
- W4308671844 date "2022-11-08" @default.
- W4308671844 modified "2023-09-24" @default.
- W4308671844 title "Theory and Application of Augmented Dimensional Analysis" @default.
- W4308671844 doi "https://doi.org/10.48550/arxiv.2211.04267" @default.
- W4308671844 hasPublicationYear "2022" @default.
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