Euler-spiral

#1 Posted: 2023/11/14 03:13:22

Valery Ochkov

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Why I can not to plot the Euler spiral curvature?
1-10-Euler-spiral.sm (175.21 KiB) downloaded 809 time(s).

#2 Posted: 2023/11/14 04:46:11

Martin Kraska

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SMath native integration is a purely numerical procedure. Derivatives are symbolic ones. You would need to replace the symbolic derivatives by approximations.

Maxima can handle the derivatives. Funny enough, Maxima can't display the integral values x(t), y(t), neither can it plot them.

But you just asked for the curvature

Euler-spiral_Maxima.sm (28.89 KiB) downloaded 800 time(s).

Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

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Valery Ochkov 2023/11/14 04:50:00, Oscar Campo 2023/11/14 10:13:00

#3 Posted: 2023/11/14 04:53:38

Valery Ochkov

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Thanks, Martin.
No solution in pure SMath?

#4 Posted: 2023/11/14 05:58:30

Martin Kraska

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Here is a solution in pure (AKA Maxima-free) SMath.

The derivatives are replaced by difference quotients with a fixed perturbation h. Sooner or later this h is too big for a precise approximation, therefore, the value of the curvature deteriorates for large values of t.
Perhaps the fixed interval integrator also is to be blamed for the loss of precision.

Another M to patent?

Euler-spiral_Kr.sm (15.13 KiB) downloaded 855 time(s).

Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

#5 Posted: 2023/11/14 06:11:13

Alvaro

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Hi. These are another two options.

1-10-Euler-spiral - option 1.sm (174.84 KiB) downloaded 839 time(s).
1-10-Euler-spiral - option 2.sm (176.58 KiB) downloaded 837 time(s).

Best regards.
Alvaro.

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Oscar Campo 2023/11/14 10:15:00, Valery Ochkov 2023/11/14 13:43:00

#6 Posted: 2023/11/14 13:45:22

Valery Ochkov

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1 users liked this post

Oscar Campo 2023/11/14 17:47:00

#7 Posted: 2023/11/14 13:52:31

Valery Ochkov

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Euler spring

#8 Posted: 2023/11/14 16:44:15

Valery Ochkov

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https://community.ptc.com/t5/Mathcad/Euler-spiral/m-p/912205/thread-id/209391

#9 Posted: 2023/11/14 18:05:37

Oscar Campo

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the Euler spring on SMath:

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Valery Ochkov 2023/11/14 18:18:00

#10 Posted: 2023/11/14 19:39:05

Jean Giraud

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Wrote
Why I can not to plot the Euler spiral curvature ?

Cornu = Euler = Fresnel = Clothoid ... all same.

Maths Spirals Euler-Cornu.sm (17.51 KiB) downloaded 813 time(s).
Maths Spirals_ANY.sm (26.77 KiB) downloaded 840 time(s).

#11 Posted: 2023/11/14 20:27:47

Jean Giraud

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Wrote
Cornu = Euler = Fresnel = Clothoid ... all same.

In the document ANY spiral ... set
c:= 0.30634896253
k:= -0.848622607416
r:= 0.25 ... immaterial, just to plot on same canvas.
You will have the Golden spiral considered Fibonacci.
Cheers ... Jean.

#12 Posted: 2023/11/15 09:00:51

Valery Ochkov

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