Error by ODEs solution

#1 Publicado: 14/12/2023 1:35:18

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Here OK Rocket-1.sm (16,79 KiB) descargado 1422 vez(es).
Here not OK Rocket-2.sm (688,11 KiB) descargado 1453 vez(es).
About the problem Study-24-How-calculate-Rocket.doc (1,95 MiB) descargado 843 vez(es).
from the book
https://www.routledge.com/25-Problems-for-STEM-Education/Ochkov/p/book/9780367345259

#2 Publicado: 14/12/2023 9:58:26

Alvaro

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Hi Valery. Just use cases() instead if() clauses.

Rocket-2.sm (688,31 KiB) descargado 1485 vez(es).

But Newton's second law is not F=ma which is an expression valid only for systems where m is constant. The general expression given by Newton is F=d(mv)/dt or F=dp/dt with p=mv the linear momentum.

Best regards.
Alvaro.

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Valery Ochkov 14/12/2023 14:13:00

#3 Publicado: 14/12/2023 14:30:08

Valery Ochkov

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Wrote
Hi Valery. Just use cases() instead if() clauses.

But Newton's second law is not F=ma which is an expression valid only for systems where m is constant. The general expression given by Newton is F=d(mv)/dt or F=dp/dt with p=mv the linear momentum.

Best regards.
Alvaro.

Thanks, Alvaro!
One questions.
How can we solve this problem with ODE as F=dp/dt, not F=m dv/dt?
Will we get others (numerical) answer?

Rocket-2-otherwise.sm (690,02 KiB) descargado 1470 vez(es).

#4 Publicado: 14/12/2023 18:32:10

Alvaro

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The speed of the rocket cannot be independent of the speed at which the propellant exits. Entering that information gives me this solution

Rocket-1.sm (20,07 KiB) descargado 1427 vez(es).

Another way of looking at it, using the equation F = d(mv)/dt, we must take into account that in a rocket the reaction force is not applied to the same body as the action force, as the 3rd Law says, and therefore the temporal derivative of the product mv must be done by changing the reference frame, which is why it is F = m dv/dt + u dm/dt, where v is the speed of the rocket with respect to the inertial reference system attached to the earth, but u is the speed of the propellant with respect to the non-inertial reference system attached to the rocket

Best regards.
Alvaro.

#5 Publicado: 14/12/2023 18:35:31

Valery Ochkov

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New question

Rocket-1.sm (734,95 KiB) descargado 1473 vez(es).

#6 Publicado: 15/12/2023 1:16:32

Alvaro

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Wrote
New question...

Hi Valery. You can't take the temporal derivative directly. Please see my previous answer explaining why I think that.

Best regards.
Alvaro.

#7 Publicado: 15/12/2023 2:39:15

Valery Ochkov

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Wrote

Wrote
New question...

Hi Valery. You can't take the temporal derivative directly. Please see my previous answer explaining why I think that.

Best regards.
Alvaro.

#8 Publicado: 15/12/2023 3:25:33

Alvaro

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Hi Valery. You're right encircling u. Its correct value is u = F/μ. Thus, the force over the rocket is F = - mg - u*dm/dt

Rocket-1.sm (23,73 KiB) descargado 1464 vez(es).

Best regards.
Alvaro.

#9 Publicado: 15/12/2023 4:04:15

Valery Ochkov

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Thanks, Alvaro.
And what about the 2-stage rocket?
Our first try
Rocket-2.sm (690,02 KiB) descargado 1518 vez(es).

#10 Publicado: 15/12/2023 4:30:05

Alvaro

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Wrote
...
And what about the 2-stage rocket?
Our first try

Hi. Your original solution for rocket-1 is ok, and that implies that the movie's solution is also ok.

I was only pointing out the way to deduce it. Writing the relationship for several stages would imply asking for derivatives for functions with cases(), which cannot be done, because although functions can be integrated with cases() or using inside the Mathcad block, they definitely cannot be derived.

So I guess the best solution is the one you gave at the beginning, simply replacing the if() with cases(). The deduction based on physical principles has already been done for one stage. Now it remains to apply the simplified result for several, which is exactly what the rocket-2 case does.

Best regards.
Alvaro.

#11 Publicado: 15/12/2023 5:00:55

Valery Ochkov

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I think it is easier to solve two equations - for two stages, and then for one (last) stage of the rocket.

#12 Publicado: 15/12/2023 6:58:19

Martin Kraska

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Analytical reference solution for h(t) (from a mechanics textbook) and with a single second order DE. in() would be even better without braces (operator form)

Rakete.sm (21,1 KiB) descargado 1443 vez(es).

Rakete2.sm (21,45 KiB) descargado 1484 vez(es).

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

#13 Publicado: 16/12/2023 15:47:47

Valery Ochkov

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I would like to publish an article about Rockets in the Journal "Physic in school".
Martin, Rasonar!
Would you like to be coauthors?
See please attach
Polet na Lunu.docx (585,34 KiB) descargado 785 vez(es).
Rakete-1.sm (16,31 KiB) descargado 1443 vez(es).
Rakete-2.sm (17,18 KiB) descargado 1447 vez(es).

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Alvaro 17/12/2023 2:04:00

#14 Publicado: 17/12/2023 2:10:50

Alvaro

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Wrote
I would like to publish an article about Rockets in the Journal "Physic in school".
Martin, Rasonar!
Would you like to be coauthors?
See please attach
Polet na Lunu.docx (585,34 KiB) descargado 785 vez(es).
Rakete-1.sm (16,31 KiB) descargado 1443 vez(es).
Rakete-2.sm (17,18 KiB) descargado 1447 vez(es).

Hi Valery. Sure. It will be a great experience.

Best regards.
Alvaro.

#15 Publicado: 17/12/2023 5:05:30

Jean Giraud

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I would like to publish an article about Rockets in the Journal "Physic in school".

The book about Holistic is the rocket model ... works fine in Smath 30405.
Once data will be collected clean, it may be interesting to collect as a function.
A good candidate may be Thiele.
The rocket system does not follow a single DE law, Like ISA.
Thiele fits ISA form - 1km ... 100 km
Jean.

#16 Publicado: 17/12/2023 5:49:57

Martin Kraska

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Wrote
I would like to publish an article about Rockets in the Journal "Physic in school".
Martin, Rasonar!
Would you like to be coauthors?
See please attach
Polet na Lunu.docx (510,06 KiB) descargado 828 vez(es).
Rakete-1.sm (16,31 KiB) descargado 1443 vez(es).
Rakete-2.sm (17,18 KiB) descargado 1447 vez(es).

Of course. If I remember correctly, some time there were examples for three-body problems earth-moon-spacecraft. Can't find it just now but that could make another co-author.

Edit: https://en.smath.com/forum/yaf_postsm76986_Mathcad-Toolbox.aspx#post76986

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

#17 Publicado: 17/12/2023 15:12:04

Valery Ochkov

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> Of course. If I remember correctly, some time there were examples for three-body problems

See see please solutions from Slava

three bodies problem

#18 Publicado: 17/12/2023 21:42:27

Jean Giraud

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Wrote
A good candidate may be Thiele.

I tried Cholesky ... Quite good.
For this 6 points Rocket from the book, Holistic works fine.
Unfortunately, we don't have an exportable formula.
Re-Conciliate the project ... Thiele
Jean

#19 Publicado: 17/12/2023 22:33:09

Valery Ochkov

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