Three-dimensional analogues of the Blasius-Chaplygin formulas
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908479281692672 |
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| author | Legatiuk, Dmitrii Orelma, Heikki |
| author_facet | Legatiuk, Dmitrii Orelma, Heikki |
| contents | The classical Blasius--Chaplygin formula provides an elegant method for calculating the lift force on a two-dimensional body in steady, irrotational flow. The key ingredient is the definition of a complex-valued potential function \begin{equation*} f(z) = φ(x, y) + \mathbf{i}ψ(x, y), \end{equation*} which can then be integrated using Cauchy's theorem along any closed contour surrounding the body. In this paper, we propose a three-dimensional extension of the classical Blasius--Chaplygin formula using quaternionic analysis. After presenting the basics of quaternionic analysis, we discuss how \emph{monogenic functions} -- the quaternionic analog of classical holomorphic functions -- can be used to describe problems in fluid dynamics. Finally, we present the Blasius--Chaplygin formula in quaternionic form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three-dimensional analogues of the Blasius-Chaplygin formulas Legatiuk, Dmitrii Orelma, Heikki Complex Variables Mathematical Physics The classical Blasius--Chaplygin formula provides an elegant method for calculating the lift force on a two-dimensional body in steady, irrotational flow. The key ingredient is the definition of a complex-valued potential function \begin{equation*} f(z) = φ(x, y) + \mathbf{i}ψ(x, y), \end{equation*} which can then be integrated using Cauchy's theorem along any closed contour surrounding the body. In this paper, we propose a three-dimensional extension of the classical Blasius--Chaplygin formula using quaternionic analysis. After presenting the basics of quaternionic analysis, we discuss how \emph{monogenic functions} -- the quaternionic analog of classical holomorphic functions -- can be used to describe problems in fluid dynamics. Finally, we present the Blasius--Chaplygin formula in quaternionic form. |
| title | Three-dimensional analogues of the Blasius-Chaplygin formulas |
| topic | Complex Variables Mathematical Physics |
| url | https://arxiv.org/abs/2508.03382 |