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OchkovVF		#1 Posted : 14 November 2023 09:13:22(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)		Why I can not to plot the Euler spiral curvature? 1-10-Euler-spiral.sm (176kb) downloaded 8 time(s).
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mkraska		#2 Posted : 14 November 2023 10:46:11(UTC)
Rank: Advanced Member Groups: Registered Joined: 15/04/2012(UTC) Posts: 1,990 Was thanked: 1128 time(s) in 724 post(s)		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 (29kb) downloaded 4 time(s).
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OchkovVF		#3 Posted : 14 November 2023 10:53:38(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)		Thanks, Martin. No solution in pure SMath?
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mkraska		#4 Posted : 14 November 2023 11:58:30(UTC)
Rank: Advanced Member Groups: Registered Joined: 15/04/2012(UTC) Posts: 1,990 Was thanked: 1128 time(s) in 724 post(s)		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 (16kb) downloaded 6 time(s). Edited by user 14 November 2023 12:11:38(UTC)  | Reason: Not specified
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Razonar		#5 Posted : 14 November 2023 12:11:13(UTC)
Rank: Advanced Member Groups: Registered Joined: 28/08/2014(UTC) Posts: 1,370 Was thanked: 833 time(s) in 527 post(s)		Hi. These are another two options. 1-10-Euler-spiral - option 1.sm (175kb) downloaded 11 time(s). 1-10-Euler-spiral - option 2.sm (177kb) downloaded 8 time(s). Best regards. Alvaro.
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OchkovVF		#6 Posted : 14 November 2023 19:45:22(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)		Edited by user 14 November 2023 21:44:38(UTC)  | Reason: Not specified
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OchkovVF		#7 Posted : 14 November 2023 19:52:31(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)		Euler spring
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OchkovVF		#8 Posted : 14 November 2023 22:44:15(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)		https://community.ptc.co.../912205/thread-id/209391
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oscampo		#9 Posted : 15 November 2023 00:05:37(UTC)
Rank: Advanced Member Groups: Registered Joined: 10/12/2009(UTC) Posts: 249 Location: Cali, Colombia Was thanked: 87 time(s) in 66 post(s)		the Euler spring on SMath:
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Jean Giraud		#10 Posted : 15 November 2023 01:39:05(UTC)
Rank: Guest Groups: Registered Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)		Originally Posted by: OchkovVF Why I can not to plot the Euler spiral curvature ? Cornu = Euler = Fresnel = Clothoid ... all same. Maths Spirals Euler-Cornu.sm (18kb) downloaded 4 time(s). Maths Spirals_ANY.sm (27kb) downloaded 4 time(s).
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Jean Giraud		#11 Posted : 15 November 2023 02:27:47(UTC)
Rank: Guest Groups: Registered Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)		Originally Posted by: Jean Giraud 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.
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OchkovVF		#12 Posted : 15 November 2023 15:00:51(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)
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Razonar		#13 Posted : 15 November 2023 16:28:26(UTC)
Rank: Advanced Member Groups: Registered Joined: 28/08/2014(UTC) Posts: 1,370 Was thanked: 833 time(s) in 527 post(s)		Hi. Using the numerical limit procedure from this post 1-10-Euler-spiral - option 2.sm (41kb) downloaded 8 time(s). Best regards. Alvaro. Edited by user 15 November 2023 17:03:22(UTC)  | Reason: Add other limits
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OchkovVF		#14 Posted : 16 November 2023 02:57:32(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)
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Razonar		#15 Posted : 16 November 2023 04:18:36(UTC)
Rank: Advanced Member Groups: Registered Joined: 28/08/2014(UTC) Posts: 1,370 Was thanked: 833 time(s) in 527 post(s)		You can get that editing the file in this post: Best regards. Alvaro.
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OchkovVF		#16 Posted : 16 November 2023 05:12:37(UTC)
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Razonar		#17 Posted : 16 November 2023 05:55:45(UTC)
Rank: Advanced Member Groups: Registered Joined: 28/08/2014(UTC) Posts: 1,370 Was thanked: 833 time(s) in 527 post(s)		Nice picture. This is a conic helicoid. HelliCone.sm (149kb) downloaded 5 time(s). Best regards. Alvaro.
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mkraska		#18 Posted : 16 November 2023 14:16:36(UTC)
Rank: Advanced Member Groups: Registered Joined: 15/04/2012(UTC) Posts: 1,990 Was thanked: 1128 time(s) in 724 post(s)		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 (273kb) downloaded 6 time(s).
		Martin Kraska Pre-configured portable distribution of SMath Studio: https://smath.com/wiki/SMath_with_Plugins.ashx
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OchkovVF		#19 Posted : 16 November 2023 14:46:37(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)		https://yandex.ru/video/...view/7434912311849987856 Knot.png (1,174kb) downloaded 7 time(s). Edited by user 16 November 2023 14:50:02(UTC)  | Reason: Not specified
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OchkovVF		#20 Posted : 16 November 2023 15:08:36(UTC)
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 349 Was thanked: 28 time(s) in 27 post(s)		Euler target
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