A Minimalist Approach to Rolling Wheels
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910220578455552 |
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| author | Slavík, Antonín Wagon, Stan |
| author_facet | Slavík, Antonín Wagon, Stan |
| contents | In 1960, G. B. Robison discovered the general equations relating roads and wheels, where either can have an unusual shape (e.g., the square wheel rolls smoothly on a catenary). But he used some inobvious assumptions regarding the meaning of rolling. Here we derive the equations for the road appropriate for a given wheel using only the single assumption that rolling occurs with no slipping. We do not require that the wheel be differentiable, so this allows the construction of a wheel-road pair when the wheel is a continuous nowhere differentiable function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03749 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Minimalist Approach to Rolling Wheels Slavík, Antonín Wagon, Stan Classical Analysis and ODEs 53A04 In 1960, G. B. Robison discovered the general equations relating roads and wheels, where either can have an unusual shape (e.g., the square wheel rolls smoothly on a catenary). But he used some inobvious assumptions regarding the meaning of rolling. Here we derive the equations for the road appropriate for a given wheel using only the single assumption that rolling occurs with no slipping. We do not require that the wheel be differentiable, so this allows the construction of a wheel-road pair when the wheel is a continuous nowhere differentiable function. |
| title | A Minimalist Approach to Rolling Wheels |
| topic | Classical Analysis and ODEs 53A04 |
| url | https://arxiv.org/abs/2604.03749 |