clothoid - SMath

#1 Publicado: 26/9/2023 2:22:21

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Continuing the topic
https://en.smath.com/forum/yaf_postst23677_Why-I-have-no.aspx

This is a clothoid or Euler spiral (https://en.wikipedia.org/wiki/Euler_spiral). It is said about it that its curvature depends linearly on its length. How to show it in SMath?
Spiral-Euler.sm (5,75 KiB) descargado 1476 vez(es).

#2 Publicado: 26/9/2023 8:41:22

Alvaro

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Hi Valery. SMath doesn't know how to handle the derivative of an integral, neither numerically nor symbolically. As workaround, you can try this approach:

Best regards.
Alvaro.

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Valery Ochkov 26/9/2023 11:21:00, Oscar Campo 26/9/2023 12:05:00

#3 Publicado: 27/9/2023 8:55:52

Jean Giraud

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Wrote
This is a clothoid or Euler spiral (https://en.wikipedia.org/wiki/Euler_spiral). It is said about it that its curvature depends linearly on its length. How to show it in SMath ?

The curvature exists in the ± 1 range. But not as you attempted.
Let my tech doctor Win 10, will attach later.
Jean.

#4 Publicado: 27/9/2023 19:06:44

Jean Giraud

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Wrote
How to show it in SMath ?

Maths Clothoid Copy.sm (53,73 KiB) descargado 1469 vez(es).

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Valery Ochkov 28/9/2023 1:28:00

#5 Publicado: 28/9/2023 3:58:26

Valery Ochkov

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Wrote

Wrote
How to show it in SMath ?

Maths Clothoid Copy.sm (53,73 KiB) descargado 1469 vez(es).

#6 Publicado: 28/9/2023 3:59:06

Valery Ochkov

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Oscar Campo 28/9/2023 9:58:00

#7 Publicado: 28/9/2023 4:19:07

Martin Kraska

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Wrote
Continuing the topic

This is a clothoid or Euler spiral (https://en.wikipedia.org/wiki/Euler_spiral). It is said about it that its curvature depends linearly on its length. How to show it in SMath?

For the attached sheet to work, the Statistical Tools plugin must be deactivated, because it's erf() shadows the Maxima function erf().

The curvature-arclength plot is easily done, yet the xy plot of the curve itself fails because Maxima isn't able to evaluate the functions x(t) and y(t).

Yet, it is not proof of linearity, just an illustration.

Spiral-Euler_Kr.sm (34,32 KiB) descargado 1468 vez(es).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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Oscar Campo 28/9/2023 9:58:00, Valery Ochkov 28/9/2023 4:22:00

#8 Publicado: 28/9/2023 11:22:42

Вячеслав Мезенцев

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Russia ☭ forever, Viacheslav N. Mezentsev

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Valery Ochkov 28/9/2023 13:07:00, Oscar Campo 28/9/2023 13:26:00

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