Derivative in Maple

#1 Pubblicato: 05/12/2023 12:53:18

Valery Ochkov

67 apprezzamenti in 713 post.

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Pendulum.sm (233,97 KiB) scaricato 1476 volta(e).

#2 Pubblicato: 05/12/2023 13:38:18

Вячеслав Мезенцев

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Ctrl+Shift+K.

Russia ☭ forever, Viacheslav N. Mezentsev

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Valery Ochkov 05/12/2023 13:54:00

#3 Pubblicato: 05/12/2023 22:44:09

Valery Ochkov

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Wrote
Ctrl+Shift+K.

Can we solve this task with SMath + Mathcad

#4 Pubblicato: 06/12/2023 00:05:11

Вячеслав Мезенцев

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Можно попробовать, если будет доступен оригинальный документ Mathcad.

Russia ☭ forever, Viacheslav N. Mezentsev

#5 Pubblicato: 06/12/2023 00:55:01

Valery Ochkov

67 apprezzamenti in 713 post.

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Можно попробовать, если будет доступен оригинальный документ Mathcad.

Pendulum-Spring.xmcd (159,03 KiB) scaricato 1501 volta(e).

#6 Pubblicato: 06/12/2023 03:09:08

Martin Kraska

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The definition of l(t) must be inside or above the Mathcad block

Federpendel-block.sm (39,22 KiB) scaricato 1464 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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Valery Ochkov 06/12/2023 04:16:00

#7 Pubblicato: 06/12/2023 05:04:43

Valery Ochkov

67 apprezzamenti in 713 post.

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My solution

Pendulum-Spring.xmcd (82,56 KiB) scaricato 1509 volta(e).

#8 Pubblicato: 06/12/2023 05:15:14

Valery Ochkov

67 apprezzamenti in 713 post.

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Animation needed

#9 Pubblicato: 06/12/2023 07:57:07

Jean Giraud

983 apprezzamenti in 6.866 post.

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Simple pendulum + animation.

ODE Pendulum Copy.sm (103,31 KiB) scaricato 1469 volta(e).

#10 Pubblicato: 06/12/2023 12:49:26

Alvaro

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Comparing with the usual elastic pendulum.

Ochkov elastic pendulum.sm (32,17 KiB) scaricato 1432 volta(e).

Best regards.
Alvaro.

2 utenti hanno apprezzato questo post

Вячеслав Мезенцев 06/12/2023 14:10:00, Valery Ochkov 06/12/2023 14:34:00

#11 Pubblicato: 06/12/2023 14:38:55

Valery Ochkov

67 apprezzamenti in 713 post.

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See please the Fig. 4.10 here
http://twt.mpei.ac.ru/ochkov/Ochkov-V-F-Engineering-Calc.pdf
Now I would like to rewrite this Russian-English book with SMath. Help me please!

#12 Pubblicato: 06/12/2023 20:02:42

Valery Ochkov

67 apprezzamenti in 713 post.

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Why I have an error in this task? Help please!
Pund-Spring.sm (15,02 KiB) scaricato 1479 volta(e).

#13 Pubblicato: 06/12/2023 21:27:58

Valery Ochkov

67 apprezzamenti in 713 post.

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More simple task
Pund.sm (11,53 KiB) scaricato 1497 volta(e).

#14 Pubblicato: 07/12/2023 06:47:42

Martin Kraska

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If F(t) is requested as result, you have to specify F'(t). k(F) is the tangential stiffness of the spring, the inverse of the tangential compliance.

Federpendel-NL.sm (13,71 KiB) scaricato 1474 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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Valery Ochkov 07/12/2023 13:02:00, Alvaro 07/12/2023 12:22:00

#15 Pubblicato: 07/12/2023 13:03:36

Valery Ochkov

67 apprezzamenti in 713 post.

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More animations
https://community.ptc.com/t5/Mathcad/One-interesting-problrm-with-shue/td-p/635149
Let create it with SMath
Слабо?

#16 Pubblicato: 07/12/2023 15:59:36

Martin Kraska

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In this version you can specify the initial force in the spring. The initial conditions for x and y are adjusted appropriately.

Federpendel-NL.sm (15,06 KiB) scaricato 1491 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

2 utenti hanno apprezzato questo post

Alvaro 08/12/2023 05:03:00, Valery Ochkov 08/12/2023 08:11:00

#17 Pubblicato: 08/12/2023 03:12:47

Jean Giraud

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Your Mathcad Given/Odesolve ... solves via Maple.
Verhulst solves wrt limits ... pretty advanced.

Inst_Verhulst.sm (27,14 KiB) scaricato 1469 volta(e).

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Valery Ochkov 08/12/2023 08:11:00

#18 Pubblicato: 08/12/2023 05:06:15

Alvaro

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The equations of motion, using Lagrange dynamics, from this post:

ElasticPendulum.sm (244,53 KiB) scaricato 1464 volta(e).

Best regards.
Alvaro.

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Valery Ochkov 08/12/2023 08:10:00, sergio 08/12/2023 23:03:00

#19 Pubblicato: 08/12/2023 07:54:19

Alvaro

1.139 apprezzamenti in 1.805 post.

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Wrote
In this version you can specify the initial force in the spring. The initial conditions for x and y are adjusted appropriately. ...

A comparison between Martin's solution and that given by the equations of motion obtained from the Lagrangian. Spoiler: both give the same result.

I'd like to point out how incredibly complicated this problem actually is, and what a series of brilliant implementations Martin makes. For example, where the hell does he get the time derivative of the force on an elastic bar when he is given only the length of the bar as a function of the force? Obviously, it is not enough to apply the theorem of the derivative of the inverse function, but you also have to have a deep knowledge of the mechanics of the system to remember something called tangential stiffness, and although it uses k to represent it, we forgive it because It's German and they are well known to use their own abbreviations. Well, actually I don't know what letter to use, because I don't remember ever using that magnitude for any practical purpose, but in Spanish literature it is quite common to use k for its inverse, which is the constant that appears in Hooke's law. Or at least I think so, because the existence of elastic bodies is actually a complication, they should all be rigid better.

Another notable thing about this example is that I would like someone to please explain to me how the hell the Viacheslav plugin manages to handle l'(t) within the equations, because I honestly didn't expect it.

Federpendel-NL - Lagrangian.sm (257,87 KiB) scaricato 1600 volta(e).

Best regards.
Alvaro.

3 utenti hanno apprezzato questo post

Valery Ochkov 08/12/2023 08:10:00, Martin Kraska 08/12/2023 15:04:00, Вячеслав Мезенцев 08/12/2023 15:35:00

#20 Pubblicato: 08/12/2023 13:00:10

Valery Ochkov

67 apprezzamenti in 713 post.

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Have you seen this plot

Forum SMath

Derivative in Maple - How insert - Messaggi