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13-Aquamarine

## Solve-Block-Solution: non linear EQN-System

Hi!

Maybe today it is much too hot and I have drunk too little water and coffee, but i can't find a stable solution for a defined problem:

I have to solve a mechanical problem (dimensioning steel cables) with the solve block including 18 equations with 18 unknowns:

It is required that the length change, the number of threads and all forces, etc. are calculated with the solver.

Please see the sketch (you can doubleclick the .exe file to view it, it's an e-drawing file) and worksheet in attach.

The Problem is: I have as many equations as unknowns and when i change the guess values, i get always different results.

Are my equations right, and do i define something double or contradictory?

Any help will be appreciated.

Thank you very much for your efforts.

Volker

Volker
1 ACCEPTED SOLUTION

Accepted Solutions
16-Pearl
(To:vlehner)

I believe you have not formulated it correctly.  If you get multiple answers that usually means there are multiple answers.  Mathcad stops as soon as it finds one solution.  Running a quick check of your results shows that all of the constraints are solved properly with your results.  Maybe TOL or CTOL would make a difference, but I doubt it.  Check the results to see what isn't making sense.

15 REPLIES 15
24-Ruby IV
(To:vlehner)

Better to have the guess value not as x:=1 y:=2 ets but as two vectors.

As here for example

13-Aquamarine
(To:ValeryOchkov)

Thanks Valery, that's cool idea!

I used the results for guess-values like you did (in Vector-Form) but i got unrealistic results although i checked my equations again after that.

Volker
24-Ruby IV
(To:vlehner)

And second!

Non linrar system can have not one solution!

13-Aquamarine
(To:ValeryOchkov)

I know this but i am wondering why there is anyway no appropriate Solution.

Volker
24-Ruby V
(To:ValeryOchkov)
 Valery Ochkov wrote: And second! Non linrar system can have not one solution! See please Given-Find Block and Guess value

I like this example of yours and its interesting to see how different algorithms chosen influence the outcome

As we see LM fails if x=0 or y=0.

24-Ruby IV
(To:Werner_E)

Thanks, Werner!

It is my Van Gogh in Mathcad!

See pleas the english variant of my old article (a chapter from my book):

Решение алгебраических уравнений и систем

And we have n real roots and plus n^2 or more complex roots!

See one picture from the article (the old good Mathcad 11 + Maple - 4 real roots):

Why "old good"?

13-Aquamarine
(To:ValeryOchkov)

Viktor
24-Ruby IV
(To:ViktorKorobov)

Почему у меня не получилось?

Why do I have not same answer?

Sorry

y^2-y^2

but x^2-y^2

24-Ruby IV
(To:Werner_E)
 Werner Exinger написал(а): As we see LM fails if x=0 or y=0.

Yes!

It is a schwarzes Kreuz from LM

24-Ruby IV
(To:Werner_E)
 Werner Exinger написал(а):

Better to have 7 roots and 7 colors - a rainbow - радуга!

Do you have this example? Слабо?

24-Ruby IV
(To:Werner_E)
 Werner Exinger написал(а): Valery Ochkov wrote: And second! Non linrar system can have not one solution! See please Given-Find Block and Guess value I like this example of yours and its interesting to see how different algorithms chosen influence the outcome As we see LM fails if x=0 or y=0.

Werner!

16-Pearl
(To:vlehner)

I believe you have not formulated it correctly.  If you get multiple answers that usually means there are multiple answers.  Mathcad stops as soon as it finds one solution.  Running a quick check of your results shows that all of the constraints are solved properly with your results.  Maybe TOL or CTOL would make a difference, but I doubt it.  Check the results to see what isn't making sense.

13-Aquamarine
(To:DJF)

Hi dferry,

Thank you!

I'll check this again.

You are concentrated to the problem and sorry for the other answes in my thread: I don't need nice animations and Van Goghs-this is out of my topic, i need solutions and that non linear systems can have multiple solutions is clear for me and can be told in one sentence !!!

Volker

Volker
13-Aquamarine
(To:DJF)

I checked all with boolean:

Of course it is all true because the solver found one solution which fits to all equations!

My Problem here is: Finding the right equation(s) for a practicable solution.

Volker
13-Aquamarine
(To:DJF)

Hi dferry,

Thank you again, i have the problem not correctly formulated. There were two Equations lost, which describe the tension completely.

When changing e.g. the guess-values for the forces, the solution keeps stable. When changing the forces to a value which is too far away from the desired solution we get unrealistic results (but the EQN-system is solved as well but at another solution point- that's ok too as far as mathematics is concerned)

Now it is solved completely.

Best Regards,

Volker

Volker
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