Euler-spiral

#1 Pubblicato: 14/11/2023 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) scaricato 1548 volta(e).

#2 Pubblicato: 14/11/2023 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) scaricato 1518 volta(e).

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

2 utenti hanno apprezzato questo post

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

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

Valery Ochkov

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Thanks, Martin.
No solution in pure SMath?

#4 Pubblicato: 14/11/2023 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) scaricato 1605 volta(e).

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

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

Alvaro

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Hi. These are another two options.

1-10-Euler-spiral - option 1.sm (174,84 KiB) scaricato 1566 volta(e).
1-10-Euler-spiral - option 2.sm (176,58 KiB) scaricato 1552 volta(e).

Best regards.
Alvaro.

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

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

Valery Ochkov

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1 utenti hanno apprezzato questo post

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

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

Valery Ochkov

67 apprezzamenti in 713 post.

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Euler spring

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

Valery Ochkov

67 apprezzamenti in 713 post.

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

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

Oscar Campo

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the Euler spring on SMath:

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

#10 Pubblicato: 14/11/2023 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) scaricato 1535 volta(e).
Maths Spirals_ANY.sm (26,77 KiB) scaricato 1622 volta(e).

#11 Pubblicato: 14/11/2023 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 Pubblicato: 15/11/2023 09:00:51

Valery Ochkov

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