One-Dimensional Mathematical Model for Kayak Propulsion
[EN] The displacement of a sprint kayak can be described by a one-dimensional mathematical model, which, in its simplest case, is analogous to the free-fall problem with quadratic drag and constant propulsion. To describe realistic cases, it is necessary to introduce a propulsion capable of reproduc...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad de León |
| Repositorio: | BULERIA. Repositorio Institucional de la Universidad de León |
| OAI Identifier: | oai:buleria.unileon.es:10612/18936 |
| Acesso em linha: | https://www.mdpi.com/2076-3417/11/21/10393 https://hdl.handle.net/10612/18936 |
| Access Level: | acceso abierto |
| Palavra-chave: | Matemáticas Kayak propulsion Analytic model Mathematical model Fourier series Periodic propulsion Reduced dimensionality models Applied physics Differential equations |
| Resumo: | [EN] The displacement of a sprint kayak can be described by a one-dimensional mathematical model, which, in its simplest case, is analogous to the free-fall problem with quadratic drag and constant propulsion. To describe realistic cases, it is necessary to introduce a propulsion capable of reproducing the characteristics of the kayak stroke, including periodicity, average force and effects of stroke frequency, among others. Addressing the problem in terms of a Fourier series allows us to separate the equation into two parts, one of which is equivalent to the constant propulsion case and results in an asymptotic expression, while the second accounts for the periodic contributions. This approach allows us to solve several cases of interest: to propose a quadrature rule for the asymptotic part that allows fast estimations; to compare results with the literature; and finally to propose a general mathematical method for this problem which could help to understand some key strategies in the kayak race. |
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