Dimensional analysis with constraints
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | |
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| _version_ | 1866908920053760000 |
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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 |