Euler-spiral

#1 Posted: 11/14/2023 3:13:22 AM

Valery Ochkov

66 likes in 671 posts.

Group: User

Why I can not to plot the Euler spiral curvature?
1-10-Euler-spiral.sm (175.21 KiB) downloaded 912 time(s).

#2 Posted: 11/14/2023 4:46:11 AM

Martin Kraska

1,332 likes in 2,240 posts.

Group: Moderator

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 922 time(s).

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

2 users liked this post

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

66 likes in 671 posts.

Group: User

Thanks, Martin.
No solution in pure SMath?

#4 Posted: 11/14/2023 5:58:30 AM

Martin Kraska

1,332 likes in 2,240 posts.

Group: Moderator

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 980 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

1,080 likes in 1,752 posts.

Group: User

Hi. These are another two options.

1-10-Euler-spiral - option 1.sm (174.84 KiB) downloaded 948 time(s).
1-10-Euler-spiral - option 2.sm (176.58 KiB) downloaded 946 time(s).

Best regards.
Alvaro.

2 users liked this post

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

66 likes in 671 posts.

Group: User

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

66 likes in 671 posts.

Group: User

Euler spring

#8 Posted: 11/14/2023 4:44:15 PM

Valery Ochkov

66 likes in 671 posts.

Group: User

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

135 likes in 309 posts.

Group: Moderator

the Euler spring on SMath:

1 users liked this post

Valery Ochkov 11/14/2023 6:18:00 PM

#10 Posted: 11/14/2023 7:39:05 PM

Jean Giraud

983 likes in 6,866 posts.

Group: User

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 929 time(s).
Maths Spirals_ANY.sm (26.77 KiB) downloaded 956 time(s).

#11 Posted: 11/14/2023 8:27:47 PM

Jean Giraud

983 likes in 6,866 posts.

Group: User

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

66 likes in 671 posts.

Group: User