Timeline for Is there an analytic formula (or even a name...) for a plane curve with curvature inversely proportional to x?
Current License: CC BY-SA 4.0
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| Feb 18, 2021 at 20:00 | comment | added | Jacob Schwartz | Thanks you. I've been reading over the document and admit to being somewhat confused, as I'm but a physicist. I see that Cooper calls these curves MacLaurin catenaries or sinusoidal catenaries. It seems like the paper could help parameterize the specific curve I'm interested in, but I don't yet understand quite how. | |
| Feb 18, 2021 at 18:38 | comment | added | user44143 | @bathalf15320, that is an answer, it shouldn’t be just a comment! | |
| Feb 18, 2021 at 17:01 | comment | added | bathalf15320 | Explicit examples of curves which have the property that the curvature is proportional to a power of the distance from the axis or the origin are given in the arXiv paper 1102.1579--they are called Mclaurin catenaries and spirals respectively and have parametric resp. polar representations $(F(t),f(t))$ resp. $r f(\theta)=1$ where $f$ is a function of the form $(\cos(d \theta))^{1/d}$ and $F$ is its primitive. They have several other interesting kinetic and geometric properties which are elucidated in the above article | |
| Feb 18, 2021 at 16:38 | history | edited | Jacob Schwartz | CC BY-SA 4.0 |
added 3 characters in body
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| Feb 18, 2021 at 16:09 | review | First posts | |||
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| Feb 18, 2021 at 16:07 | history | asked | Jacob Schwartz | CC BY-SA 4.0 |