Euler-spiral

#1 Posted: 11/14/2023 3:13:22 AM

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 727 time(s).

#2 Posted: 11/14/2023 4:46:11 AM

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 722 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 11/14/2023 4:50:00 AM, Oscar Campo 11/14/2023 10:13:00 AM

#3 Posted: 11/14/2023 4:53:38 AM

Valery Ochkov

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Thanks, Martin.
No solution in pure SMath?

#4 Posted: 11/14/2023 5:58:30 AM

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 769 time(s).

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

#5 Posted: 11/14/2023 6:11:13 AM

Alvaro Diaz Falconi

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Hi. These are another two options.

1-10-Euler-spiral - option 1.sm (174.84 KiB) downloaded 774 time(s).
1-10-Euler-spiral - option 2.sm (176.58 KiB) downloaded 760 time(s).

Best regards.
Alvaro.

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Oscar Campo 11/14/2023 10:15:00 AM, Valery Ochkov 11/14/2023 1:43:00 PM

#6 Posted: 11/14/2023 1:45:22 PM

Valery Ochkov

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1 users liked this post

Oscar Campo 11/14/2023 5:47:00 PM

#7 Posted: 11/14/2023 1:52:31 PM

Valery Ochkov

62 likes in 666 posts.

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Euler spring

#8 Posted: 11/14/2023 4:44:15 PM

Valery Ochkov

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

#9 Posted: 11/14/2023 6:05:37 PM

Oscar Campo

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the Euler spring on SMath:

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Valery Ochkov 11/14/2023 6:18:00 PM

#10 Posted: 11/14/2023 7:39:05 PM

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 737 time(s).
Maths Spirals_ANY.sm (26.77 KiB) downloaded 761 time(s).

#11 Posted: 11/14/2023 8:27:47 PM

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: 11/15/2023 9:00:51 AM

Valery Ochkov

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