Double pendulum model and animation

#1 Posted: 10/29/2025 9:15:19 AM

Valery Ochkov

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Hi friends!
Now I am on the forum again!
Anime2.sm (55.59 KiB) downloaded 55 time(s).

But the model is not correct. See please Alvaro model!

Edited 10/30/2025 7:22:14 PM

#2 Posted: 10/29/2025 10:45:45 AM

Вячеслав Мезенцев

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Using X-Y Plot

Anime2-xyplot.sm (57.84 KiB) downloaded 49 time(s).

Russia ☭ forever, Viacheslav N. Mezentsev

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sergio 10/29/2025 2:50:17 PM

#3 Posted: 10/29/2025 11:14:52 AM

Valery Ochkov

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Thanks, Слава!

Edited 10/29/2025 1:53:54 PM

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Alvaro Diaz Falconi 10/30/2025 7:04:33 AM

#4 Posted: 10/29/2025 1:56:31 PM

Valery Ochkov

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Anime-x-y-plot.sm (18.24 KiB) downloaded 46 time(s).
And where here is a bug?

#5 Posted: 10/29/2025 2:01:44 PM

Вячеслав Мезенцев

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Vector t must be defined below before the component.
The animation feature is still being developed when I have time for it.

Edited 10/29/2025 2:05:45 PM

Russia ☭ forever, Viacheslav N. Mezentsev

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Alvaro Diaz Falconi 10/30/2025 7:04:42 AM

#6 Posted: 10/29/2025 5:02:10 PM

Valery Ochkov

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Слава, а когда этот новая версия плагина появилась?

#7 Posted: 10/29/2025 6:19:29 PM

Вячеслав Мезенцев

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Quote
Слава, а когда этот новая версия плагина появилась?

В конце лета.

Edited 10/29/2025 6:21:02 PM

Russia ☭ forever, Viacheslav N. Mezentsev

#8 Posted: 10/30/2025 7:07:54 AM

Alvaro Diaz Falconi

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Hi. My approach to solving the double pendulum problem.

double_pendulum.sm (75.92 KiB) downloaded 67 time(s).

Best regards.
Alvaro.

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Valery Ochkov 10/30/2025 7:45:32 AM, Вячеслав Мезенцев 10/30/2025 9:13:40 AM, sergio 10/30/2025 12:18:26 PM

#9 Posted: 10/30/2025 1:32:00 PM

Valery Ochkov

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Newton vs Lagrange
Pendulum-2.xmcd (119.12 KiB) downloaded 40 time(s).

#10 Posted: 10/30/2025 6:31:11 PM

Valery Ochkov

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My little edit

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Alvaro Diaz Falconi 10/31/2025 4:29:45 AM

#11 Posted: 10/30/2025 7:33:11 PM

Valery Ochkov

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Triple pendulum - see errors at the second haft of time interval.
Pendulum-3-for-SMath.xmcd (220.62 KiB) downloaded 36 time(s).

Edited 10/30/2025 7:39:16 PM

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Alvaro Diaz Falconi 10/31/2025 5:05:16 AM

#12 Posted: 10/31/2025 5:03:31 AM

Alvaro Diaz Falconi

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Hi. Using pure SMath code to deduce the equations of motion from the Lagrangian, with the functions in this post: https://smath.com/en-US/forum/topic/AeeMSM/Using-differentials.

double_pendulum_lagrangian.sm (174.64 KiB) downloaded 33 time(s).

double_pendulum_lagrangian.pdf (503.4 KiB) downloaded 34 time(s).

Best regards.
Alvaro.

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Valery Ochkov 10/31/2025 7:37:56 AM, sergio 10/31/2025 8:48:37 AM

#13 Posted: 10/31/2025 5:10:58 AM

Alvaro Diaz Falconi

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Wrote
Triple pendulum - see errors at the second haft of time interval.

I no longer use Mathcad, except on rare occasions, when I rely on Mathcad version 11, which I consider the last decent version. So I can't see the triple pendulum file. And I suppose this is the situation for many SMath users who no longer have Mathcad readily available. But more than worrying about the conservation of energy, which seems to be a problem with the numerical method used, I'm more surprised to see how the future affects the past, since the animation shouldn't alter the trajectories already described by the particles as time passes.

This is my approach to the triple pendulum.

triple_pendulum_lagrangian.sm (135.01 KiB) downloaded 41 time(s).

triple_pendulum_lagrangian.pdf (248.09 KiB) downloaded 43 time(s).

Best regards.
Alvaro.

Edited 10/31/2025 6:13:23 AM

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Вячеслав Мезенцев 10/31/2025 7:18:43 AM, Valery Ochkov 10/31/2025 7:38:10 AM

#14 Posted: 10/31/2025 7:35:30 AM

Valery Ochkov

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Wrote

I no longer use Mathcad,

See pls pdf
Pendulum-3-for-SMath.pdf (589.25 KiB) downloaded 38 time(s).

Edited 10/31/2025 7:38:52 AM

#15 Posted: 10/31/2025 8:37:45 AM

Alvaro Diaz Falconi

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Wrote
See pls pdf

With those values:

triple_pendulum_lagrangian.sm (159.26 KiB) downloaded 37 time(s).

Best regards.
Alvaro.

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Valery Ochkov 10/31/2025 10:39:04 AM

#16 Posted: 10/31/2025 10:38:47 AM

Valery Ochkov

62 likes in 652 posts.

Group: User

Wrote

Wrote

I'm more surprised to see how the future affects the past, since the animation shouldn't alter the trajectories already described by the particles as time passes.
Best regards.
Alvaro.

For me too!

#17 Posted: 11/1/2025 1:52:48 AM

Valery Ochkov

62 likes in 652 posts.

Group: User

Wrote

Wrote
See pls pdf

With those values:

Best regards.
Alvaro.

One my plot:
Change of three types of energy of a swinging pendulum on an elastic suspension - SE - the spring energy

Edited 11/1/2025 1:55:02 AM

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