Euler-spiral - Сообщения
#1 Опубликовано: 14.11.2023 03:13:22
#2 Опубликовано: 14.11.2023 04:46:11
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
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
Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx
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#3 Опубликовано: 14.11.2023 04:53:38
Thanks, Martin.
No solution in pure SMath?
No solution in pure SMath?
#4 Опубликовано: 14.11.2023 05:58:30
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
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
Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx
#5 Опубликовано: 14.11.2023 06:11:13
Hi. These are another two options.
1-10-Euler-spiral - option 1.sm
1-10-Euler-spiral - option 2.sm
Best regards.
Alvaro.
1-10-Euler-spiral - option 1.sm
1-10-Euler-spiral - option 2.sm
Best regards.
Alvaro.
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#6 Опубликовано: 14.11.2023 13:45:22
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Oscar Campo 14.11.2023 17:47:00
#7 Опубликовано: 14.11.2023 13:52:31
Euler spring
#8 Опубликовано: 14.11.2023 16:44:15
https://community.ptc.com/t5/Mathcad/Euler-spiral/m-p/912205/thread-id/209391
#9 Опубликовано: 14.11.2023 18:05:37
the Euler spring on SMath:
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Valery Ochkov 14.11.2023 18:18:00
#10 Опубликовано: 14.11.2023 19:39:05
Why I can not to plot the Euler spiral curvature ?
Cornu = Euler = Fresnel = Clothoid ... all same.
Maths Spirals Euler-Cornu.sm
Maths Spirals_ANY.sm
#11 Опубликовано: 14.11.2023 20:27:47
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 Опубликовано: 15.11.2023 09:00:51
#13 Опубликовано: 15.11.2023 10:28:26
Hi. Using the numerical limit procedure from this post
1-10-Euler-spiral - option 2.sm
Best regards.
Alvaro.
1-10-Euler-spiral - option 2.sm
Best regards.
Alvaro.
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Valery Ochkov 15.11.2023 12:44:00
#14 Опубликовано: 15.11.2023 20:57:32
#16 Опубликовано: 15.11.2023 23:12:37
#18 Опубликовано: 16.11.2023 08:16:36
The plots are interactive (drag to rotate, Ctrl-Mousewheel to zoom). Yet, they are not really performant, takes approx. 3 seconds to update.
knots.sm
knots.sm
Martin KraskaPre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx
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Valery Ochkov 16.11.2023 08:51:00
#19 Опубликовано: 16.11.2023 08:46:37
https://yandex.ru/video/preview/7434912311849987856
#20 Опубликовано: 16.11.2023 09:08:36
Euler target
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