Double pendulum model and animation

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

Valery Ochkov

67 me gusta en 713 mensajes.

Grupo: User

Hi friends!
Now I am on the forum again!
Anime2.sm (55,59 KiB) descargado 1037 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

1.558 me gusta en 1.868 mensajes.

Grupo: Moderator

Using X-Y Plot

Anime2-xyplot.sm (57,84 KiB) descargado 1074 vez(es).

Russia ☭ forever, Viacheslav N. Mezentsev

A 2 usuarios les gustó este mensaje

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

67 me gusta en 713 mensajes.

Grupo: User

Thanks, Слава!

Editado 29/10/2025 13:53:54

A 1 usuarios les gustó este mensaje

Alvaro 30/10/2025 7:04:33

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

Valery Ochkov

67 me gusta en 713 mensajes.

Grupo: User

Anime-x-y-plot.sm (18,24 KiB) descargado 998 vez(es).
And where here is a bug?

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

Вячеслав Мезенцев

1.558 me gusta en 1.868 mensajes.

Grupo: Moderator

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

A 1 usuarios les gustó este mensaje

Alvaro 30/10/2025 7:04:42

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

Valery Ochkov

67 me gusta en 713 mensajes.

Grupo: User

Слава, а когда этот новая версия плагина появилась?

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

Вячеслав Мезенцев

1.558 me gusta en 1.868 mensajes.

Grupo: Moderator

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

1.139 me gusta en 1.805 mensajes.

Grupo: User

Hi. My approach to solving the double pendulum problem.

double_pendulum.sm (75,92 KiB) descargado 1084 vez(es).

Best regards.
Alvaro.

A 3 usuarios les gustó este mensaje

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

67 me gusta en 713 mensajes.

Grupo: User

Newton vs Lagrange
Pendulum-2.xmcd (119,12 KiB) descargado 1058 vez(es).

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

Valery Ochkov

67 me gusta en 713 mensajes.

Grupo: User

My little edit

A 1 usuarios les gustó este mensaje

Alvaro 31/10/2025 4:29:45

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

Valery Ochkov

67 me gusta en 713 mensajes.

Grupo: User

Triple pendulum - see errors at the second haft of time interval.
Pendulum-3-for-SMath.xmcd (220,62 KiB) descargado 1139 vez(es).

Editado 30/10/2025 19:39:16

A 1 usuarios les gustó este mensaje

Alvaro 31/10/2025 5:05:16

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

Alvaro

1.139 me gusta en 1.805 mensajes.

Grupo: User

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 1026 vez(es).

double_pendulum_lagrangian.pdf (503,4 KiB) descargado 780 vez(es).

Best regards.
Alvaro.

A 2 usuarios les gustó este mensaje

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

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

Alvaro

1.139 me gusta en 1.805 mensajes.

Grupo: User

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 1002 vez(es).

triple_pendulum_lagrangian.pdf (248,09 KiB) descargado 639 vez(es).

Best regards.
Alvaro.

Editado 31/10/2025 6:13:23

A 2 usuarios les gustó este mensaje

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

67 me gusta en 713 mensajes.

Grupo: User

Wrote

I no longer use Mathcad,

See pls pdf
Pendulum-3-for-SMath.pdf (589,25 KiB) descargado 680 vez(es).

Editado 31/10/2025 7:38:52

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

Alvaro

1.139 me gusta en 1.805 mensajes.

Grupo: User

Wrote
See pls pdf

With those values:

triple_pendulum_lagrangian.sm (159,26 KiB) descargado 1032 vez(es).

Best regards.
Alvaro.

A 1 usuarios les gustó este mensaje

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

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

Valery Ochkov

67 me gusta en 713 mensajes.

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

Valery Ochkov

67 me gusta en 713 mensajes.

Grupo: 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

Editado 1/11/2025 1:55:02

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

Valery Ochkov

67 me gusta en 713 mensajes.

Grupo: User

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

1.139 me gusta en 1.805 mensajes.

Grupo: User

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 1014 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.

A 1 usuarios les gustó este mensaje

Valery Ochkov 6/11/2025 5:16:18

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

Valery Ochkov

67 me gusta en 713 mensajes.

Grupo: 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!

Foro SMath

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