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Hi Valery. Just use cases() instead if() clauses.   Rocket-2.sm (689kb) downloaded 6 time(s).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. Edited by user 14 December 2023 16:37:36(UTC)
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 1 user thanked Razonar for this useful post.
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Rank: Advanced Member Groups: Registered, Advanced Member Joined: 06/04/2023(UTC) Posts: 339 Was thanked: 26 time(s) in 25 post(s)
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Originally Posted by: Razonar  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 (691kb) downloaded 2 time(s).Edited by user 14 December 2023 21:01:15(UTC)
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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 (21kb) downloaded 4 time(s). 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. Edited by user 15 December 2023 01:09:20(UTC)
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Originally Posted by: OchkovVF 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.
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Originally Posted by: Razonar Originally Posted by: OchkovVF 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. 
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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 (24kb) downloaded 6 time(s).Best regards. Alvaro.
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Thanks, Alvaro. And what about the 2-stage rocket? Our first try Rocket-2.sm (691kb) downloaded 6 time(s).
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Originally Posted by: OchkovVF ...
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.
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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.
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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 (586kb) downloaded 3 time(s). Rakete-1.sm (17kb) downloaded 6 time(s). Rakete-2.sm (18kb) downloaded 6 time(s).Edited by user 17 December 2023 06:52:02(UTC)
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Originally Posted by: OchkovVF 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 (586kb) downloaded 3 time(s). Rakete-1.sm (17kb) downloaded 6 time(s). Rakete-2.sm (18kb) downloaded 6 time(s). Hi Valery. Sure. It will be a great experience. Best regards. Alvaro.
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Originally Posted by: OchkovVF 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.
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Originally Posted by: OchkovVF 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 (511kb) downloaded 0 time(s). Rakete-1.sm (17kb) downloaded 6 time(s). Rakete-2.sm (18kb) downloaded 6 time(s). 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/for...d-Toolbox.aspx#post76986Edited by moderator 19 December 2023 04:37:51(UTC)
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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
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Originally Posted by: Jean Giraud 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
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Razonar
Hi Valery. Sure. It will be a great experience.
Best regards.
Alvaro.
[/quote wrote:
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3 stages variation.  Checking with Tsiolkovsky rocket equation in a gravitational field with several stages  Rakete-3.sm (47kb) downloaded 6 time(s).Best regards. Alvaro. Edited by user 18 December 2023 16:39:32(UTC)
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