Euler-spiral

#1 Posted: 2 years ago

Valery Ochkov

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Why I can not to plot the Euler spiral curvature?
1-10-Euler-spiral.sm (175 KiB) downloaded 111 time(s).

#2 Posted: 2 years ago

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 KiB) downloaded 106 time(s).

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

2 users liked this post

Valery Ochkov 2 years ago, Oscar Campo 2 years ago

#3 Posted: 2 years ago

Valery Ochkov

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Thanks, Martin.
No solution in pure SMath?

#4 Posted: 2 years ago

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 KiB) downloaded 105 time(s).

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

#5 Posted: 2 years ago

Alvaro Diaz Falconi

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Hi. These are another two options.

1-10-Euler-spiral - option 1.sm (174 KiB) downloaded 115 time(s).
1-10-Euler-spiral - option 2.sm (176 KiB) downloaded 113 time(s).

Best regards.
Alvaro.

2 users liked this post

Oscar Campo 2 years ago, Valery Ochkov 2 years ago

#6 Posted: 2 years ago

Valery Ochkov

55 likes in 634 posts.

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1 users liked this post

Oscar Campo 2 years ago

#7 Posted: 2 years ago

Valery Ochkov

55 likes in 634 posts.

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Euler spring

#8 Posted: 2 years ago

Valery Ochkov

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

#9 Posted: 2 years ago

Oscar Campo

124 likes in 298 posts.

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the Euler spring on SMath:

1 users liked this post

Valery Ochkov 2 years ago

#10 Posted: 2 years ago

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 KiB) downloaded 118 time(s).
Maths Spirals_ANY.sm (26 KiB) downloaded 108 time(s).

#11 Posted: 2 years ago

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: 2 years ago

Valery Ochkov

55 likes in 634 posts.

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