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 178 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 182 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 173 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 223 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 162 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 173 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 173 time(s).

double_pendulum_lagrangian.pdf (503.4 KiB) downloaded 95 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 165 time(s).

triple_pendulum_lagrangian.pdf (248.09 KiB) downloaded 115 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 94 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 170 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 666 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 666 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

#18 Posted: 11/5/2025 7:01:02 AM

Valery Ochkov

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Alvaro, hi!
Is it posibble to solve the single pendulun problem with Lagrangian and rkfixed but without the al_nleqsolve function?

Edited 11/5/2025 8:29:15 AM

#19 Posted: 11/6/2025 4:03:01 AM

Alvaro Diaz Falconi

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Hi Valery. For the single pendulum you can get the lagrangian from the olf post about differentials ( https://smath.com/en-US/forum/topic/AeeMSM/Using-differentials ) It's very simple and doesn't require much processing to use rkfixed.

For the double pendulum, you can use Newton-Raphson to solve the system within the function D. Here, a very simple version of the method is used.

double_pendulum_lagrangian-NR.sm (178.15 KiB) downloaded 143 time(s).

Something similar applies to the pendulum with a spring. Note that the Lagrange equations become somewhat complicated because I use the x,y coordinates to calculate the kinetic energy, and SMath cannot simplify trigonometric functions. However, if you use r, θ' (in green), the equations of motion are greatly simplified. But that breaks the principle that the program should do the calculations, not the user.

Best regards.
Alvaro.

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Valery Ochkov 11/6/2025 5:16:18 AM

#20 Posted: 11/6/2025 11:47:20 AM

Valery Ochkov

62 likes in 666 posts.

Group: User

Wrote
Hi Valery. For the single pendulum you can get the lagrangian from the olf post about differentials ( https://smath.com/en-US/forum/topic/AeeMSM/Using-differentials ) It's very simple and doesn't require much processing to use rkfixed.
Alvaro.

Hi Alvaro!

Can you create this simple sm-file with animation? Single pendulum!
Thanks!

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Double pendulum model and animation - Is the model correct? - Messages