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 1375 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 1348 time(s).

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

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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 1422 time(s).

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

#5 Posted: 11/14/2023 6:11:13 AM

Alvaro

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Hi. These are another two options.

1-10-Euler-spiral - option 1.sm (174.84 KiB) downloaded 1375 time(s).
1-10-Euler-spiral - option 2.sm (176.58 KiB) downloaded 1350 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

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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 1377 time(s).
Maths Spirals_ANY.sm (26.77 KiB) downloaded 1432 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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