Double pendulum

#1 Posted: 9/20/2026 10:08:09 AM

Valery Ochkov

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I feel the model is not correct - help please!
Pendulum-2-animation.sm (22.59 KiB) downloaded 187 time(s).

Edited 9/20/2026 10:09:28 AM

#2 Posted: 9/21/2026 11:02:24 AM

Alvaro

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Hi Valery. The system is coupled. This is a way to solve it.

double_pendulum_lagrangian.sm (122.44 KiB) downloaded 187 time(s).
double_pendulum_lagrangian.pdf (637.78 KiB) downloaded 130 time(s).

Best regards.
Alvaro.

2 users liked this post

ioan92 10/9/2026 7:34:51 PM, Valery Ochkov 9/21/2026 4:39:03 PM

#3 Posted: 9/21/2026 2:02:10 PM

Вячеслав Мезенцев

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Yes, that is correct; I previously reported on the limitations regarding the systems.

The algorithm does not currently classify the task, so issues may arise with complex problems that the current method cannot solve. It might produce a plausible-looking solution that does not actually address the problem at hand.

Russia ☭ forever, Viacheslav N. Mezentsev

#4 Posted: 9/21/2026 4:47:18 PM

Valery Ochkov

66 likes in 700 posts.

Group: User

Thanks, Alvaro.
It reminds me of an old joke.
A funeral. A passerby asks, "Who are they burying?"
"That guy lying in the coffin."
That was a mathematician's answer—completely accurate and completely useless.

Mathcad 15

Edited 9/21/2026 4:53:09 PM

#5 Posted: 9/22/2026 10:43:08 AM

Alvaro

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If mathematics is a tautology, then life must be one too. That joke reminds me of the one a plant process engineer played on me when I went to get the bourdon gauge I was supposed to install. Without a word, he handed me a brown box. That was when I have the bad idea of asking what was inside. His answer was that it contained a mechanical device that measures fluid pressure using a curved, flattened metal tube that straightens as internal pressure increases, driving an indicator needle across a calibrated dial.

The RKA function includes the necessary procedures to solve hard coupled systems.

double_pendulum_RKA.pdf (483.53 KiB) downloaded 123 time(s).
double_pendulum_RKA.sm (43.57 KiB) downloaded 184 time(s).

Best regards.
Alvaro.

2 users liked this post

Valery Ochkov 9/22/2026 12:25:43 PM, ioan92 10/9/2026 7:38:29 PM

#6 Posted: 10/8/2026 11:18:22 AM

Valery Ochkov

66 likes in 700 posts.

Group: User

Thanks, Alvaro!

But I cannnot create five f(t) plots:
Potential energy of pendulum #1
Kynetic energy of pendulum #1
Potential energy of pendulum #2
Kynetic energy of pendulum #2
Sum of energies for the verify the model and ODEs solver. Must be const.
Help please!

Edited 10/8/2026 11:18:52 AM

#7 Posted: 10/9/2026 1:06:49 AM

Alvaro

1,132 likes in 1,801 posts.

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Hi Valery. This is a way. You can plot the time in T versus U, K or U+K. The plot in the figure shows that the energy is constant. In this case also, the total energy is the hamiltonian.

double_pendulum_RKA.sm (49.21 KiB) downloaded 14 time(s).

Best regards.
Alvaro.

Edited 10/9/2026 1:19:29 AM

1 users liked this post

ioan92 10/10/2026 6:59:13 PM

#8 Posted: 10/9/2026 8:11:32 PM

ioan92

181 likes in 123 posts.

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Butterfly_Effect_Example.pptx (999.46 KiB) downloaded 7 time(s).

Hi Alvaro & Valery,

I enjoyed the matematical results of yours developements, without following all details.

I propose you a problem, dealing with the Butterfly Effect on a double pendulum - after some cycles, the 2 pendulums becoms distinct. Attached there is a simple gif file

Do to others as you would like them to do to you! Knowledge is of no value unless you put it into practice - Chekhov

#9 Posted: 10/10/2026 12:03:48 AM

Alvaro

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Hi Ioan. Something like this.

double_pendulum_RKA Butterfly Effect.sm (50.58 KiB) downloaded 11 time(s).

Best regards.
Alvaro.

4 users liked this post

Valery Ochkov 10/10/2026 5:45:18 AM, sergio 10/10/2026 8:51:15 AM, ioan92 10/10/2026 12:34:44 PM, Вячеслав Мезенцев 10/10/2026 4:02:19 PM

#10 Posted: 10/10/2026 12:30:41 PM

ioan92

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Group: User

Ooo it's wonderful!!!

My dumb explanation is that time delay generate between the 2 instances generate different precision in the solution graphics and hence the graphical difference (?).

Alvaro - All my thanks for your proverbial attention,

Have a nice WE,
Ioan

Do to others as you would like them to do to you! Knowledge is of no value unless you put it into practice - Chekhov

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Alvaro 10/10/2026 7:03:11 PM

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