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Bibliographic Details
Main Author: Miyamoto, Umpei
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.21527
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author Miyamoto, Umpei
author_facet Miyamoto, Umpei
contents We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both dimensional relations and constraints in logarithmic variables, the problem is reduced to a linear structure. This formulation yields a simple count of independent dimensionless quantities and, more importantly, a purely algebraic procedure to eliminate redundant ones without trial and error. The method is especially effective for systems with implicit or multiple constraints, and is illustrated with the classical drag force problem.
format Preprint
id arxiv_https___arxiv_org_abs_2603_21527
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Dimensional analysis with constraints
Miyamoto, Umpei
Mathematical Physics
Fluid Dynamics
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both dimensional relations and constraints in logarithmic variables, the problem is reduced to a linear structure. This formulation yields a simple count of independent dimensionless quantities and, more importantly, a purely algebraic procedure to eliminate redundant ones without trial and error. The method is especially effective for systems with implicit or multiple constraints, and is illustrated with the classical drag force problem.
title Dimensional analysis with constraints
topic Mathematical Physics
Fluid Dynamics
url https://arxiv.org/abs/2603.21527