Double pendulum model and animation

#1 Publicado: 29/10/2025 9:15:19

Valery Ochkov

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Hi friends!
Now I am on the forum again!
Anime2.sm (55,59 KiB) descargado 1035 vez(es).

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

Editado 30/10/2025 19:22:14

#2 Publicado: 29/10/2025 10:45:45

Вячеслав Мезенцев

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Using X-Y Plot

Anime2-xyplot.sm (57,84 KiB) descargado 1071 vez(es).

Russia ☭ forever, Viacheslav N. Mezentsev

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sergio 29/10/2025 14:50:17, Ricardo_Herrera 3/1/2026 14:15:17

#3 Publicado: 29/10/2025 11:14:52

Valery Ochkov

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Thanks, Слава!

Editado 29/10/2025 13:53:54

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Alvaro 30/10/2025 7:04:33

#4 Publicado: 29/10/2025 13:56:31

Valery Ochkov

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Anime-x-y-plot.sm (18,24 KiB) descargado 996 vez(es).
And where here is a bug?

#5 Publicado: 29/10/2025 14:01:44

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.

Editado 29/10/2025 14:05:45

Russia ☭ forever, Viacheslav N. Mezentsev

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Alvaro 30/10/2025 7:04:42

#6 Publicado: 29/10/2025 17:02:10

Valery Ochkov

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Слава, а когда этот новая версия плагина появилась?

#7 Publicado: 29/10/2025 18:19:29

Вячеслав Мезенцев

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Citar
Слава, а когда этот новая версия плагина появилась?

В конце лета.

Editado 29/10/2025 18:21:02

Russia ☭ forever, Viacheslav N. Mezentsev

#8 Publicado: 30/10/2025 7:07:54

Alvaro

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Hi. My approach to solving the double pendulum problem.

double_pendulum.sm (75,92 KiB) descargado 1082 vez(es).

Best regards.
Alvaro.

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

#9 Publicado: 30/10/2025 13:32:00

Valery Ochkov

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Newton vs Lagrange
Pendulum-2.xmcd (119,12 KiB) descargado 1056 vez(es).

#10 Publicado: 30/10/2025 18:31:11

Valery Ochkov

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My little edit

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Alvaro 31/10/2025 4:29:45

#11 Publicado: 30/10/2025 19:33:11

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) descargado 1138 vez(es).

Editado 30/10/2025 19:39:16

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Alvaro 31/10/2025 5:05:16

#12 Publicado: 31/10/2025 5:03:31

Alvaro

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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) descargado 1023 vez(es).

double_pendulum_lagrangian.pdf (503,4 KiB) descargado 778 vez(es).

Best regards.
Alvaro.

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

#13 Publicado: 31/10/2025 5:10:58

Alvaro

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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) descargado 1000 vez(es).

triple_pendulum_lagrangian.pdf (248,09 KiB) descargado 638 vez(es).

Best regards.
Alvaro.

Editado 31/10/2025 6:13:23

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

#14 Publicado: 31/10/2025 7:35:30

Valery Ochkov

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Wrote

I no longer use Mathcad,

See pls pdf
Pendulum-3-for-SMath.pdf (589,25 KiB) descargado 679 vez(es).

Editado 31/10/2025 7:38:52

#15 Publicado: 31/10/2025 8:37:45

Alvaro

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Wrote
See pls pdf

With those values:

triple_pendulum_lagrangian.sm (159,26 KiB) descargado 1030 vez(es).

Best regards.
Alvaro.

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Valery Ochkov 31/10/2025 10:39:04

#16 Publicado: 31/10/2025 10:38:47

Valery Ochkov

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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 Publicado: 1/11/2025 1:52:48

Valery Ochkov

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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

Editado 1/11/2025 1:55:02

#18 Publicado: 5/11/2025 7:01:02

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?

Editado 5/11/2025 8:29:15

#19 Publicado: 6/11/2025 4:03:01

Alvaro

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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) descargado 1012 vez(es).

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 6/11/2025 5:16:18

#20 Publicado: 6/11/2025 11:47:20

Valery Ochkov

67 me gusta en 713 mensajes.

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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!

Foro SMath

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