clothoid - SMath

#1 Posted: 9/26/2023 2:22:21 AM

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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 KiB) downloaded 29 time(s).

#2 Posted: 9/26/2023 8:41:22 AM

Alvaro Diaz Falconi

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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 9/26/2023 11:21:00 AM, Oscar Campo 9/26/2023 12:05:00 PM

#3 Posted: 9/27/2023 8:55:52 AM

Jean Giraud

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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 Posted: 9/27/2023 7:06:44 PM

Jean Giraud

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How to show it in SMath ?

Maths Clothoid Copy.sm (53 KiB) downloaded 23 time(s).

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

#5 Posted: 9/28/2023 3:58:26 AM

Valery Ochkov

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Wrote
How to show it in SMath ?

Maths Clothoid Copy.sm (53 KiB) downloaded 23 time(s).

#6 Posted: 9/28/2023 3:59:06 AM

Valery Ochkov

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

#7 Posted: 9/28/2023 4:19:07 AM

Martin Kraska

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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.