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08-28-2019
07:38 PM

08-28-2019
07:38 PM

Re: Best solution in Mathcad needed!

>No, its not necessary

Well, since Valery didn't define 'best solution' it may be necessary. We don't know what the scoring system is. If it's number of individual calculations required I suspect I win (or would with a larger trial sample).

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08-28-2019
07:50 PM

08-28-2019
07:50 PM

Re: Best solution in Mathcad needed!

@DJF wrote:

>No, its not necessary

Well, since Valery didn't define 'best solution' it may be necessary. We don't know what the scoring system is.

Neither does Valery, I guess 😉

He is known for changing the rules in-midst of a thread, but finally he will usually find the correct solution 🙂

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08-29-2019
03:32 AM

08-29-2019
03:32 AM

Re: Best solution in Mathcad needed!

And what about this solution?

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08-29-2019
04:00 AM

08-29-2019
04:00 AM

Re: Best solution in Mathcad needed!

@ValeryOchkov wrote:

And what about this solution?

I don't see why you call it a "solution" - you sure see the discrepancy.

I also wonder what you are looking for, what the new goal of this thread should be.

From your post yesterday I thought you were interested to find out why your solve block fails or returns wrong values and how you could fix this. So I tried to provide you with the correct solution to compare with and some tools which might help in finding out whats going on.

Now you post a significantly different sheet which again returns wrong solutions. Why? What is it you want to find at the end?

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08-30-2019
02:25 AM

08-30-2019
02:25 AM

Re: Best solution in Mathcad needed!

Update. All that remains is to do the animation:

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08-30-2019
02:46 AM

08-30-2019
02:46 AM

Re: Best solution in Mathcad needed!

I am tormented by doubts. It seems to me that in this zone there is either no solution or more than one solution!

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08-30-2019
03:42 AM

08-30-2019
03:42 AM

Re: Best solution in Mathcad needed!

A different approach to the problem, but with the same previous results:

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08-30-2019
04:44 AM

08-30-2019
04:44 AM

Re: Best solution in Mathcad needed!

@ValeryOchkov wrote:

The reason you get no or multiple results is because your solve block equations seem not to be well conditioned. Guess you need additional or other constraints to make the solve block work OK within the full valid range for CD. You sure know about this problem from your various experiments with different catenaries

.

As long as we demand that P has to be inside the quadrilateral there is exactly one solution (which is also shown by my animation).

You should try to calculate the coordinates of the point P from the solution lengths your methods give you and check, if the point is inside and if two initial angles (you have to calculate them with the coordinates of P) are still correct.

You should see that the second "solutions" you get are not really solutions as they violate either the rule that the point is inside or the angles are wrong.

It should be clear that, if CD changes, P is moving on a circle from D (for CD=0) to B (for CD approx. 39.434) as it has always to be seen at an angle of 165° from the segment BD. There is no solution for P inside the quadrilateral for CD > 39.434.

Create an animation using your calculation methods where CD changes from 0 up to 40 and show the quadrilateral, P and the calculated(!) angles psi and theta.

And .... if you really think that there may be no or two solution for, lets say, CD=9, then take a piece of paper, ruler pencil and compass and manually try to construct a solution. The two circles you have to intersect in doing so will intersect in C and P and I am pretty sure that there will be no third point of intersection and that P will be inside the quadrilateral - so you will end up with a unique solution.

I suggested doing the construction manually with pen and paper because to me that would be just more satisfying than doing it with a CAD or a program like GeoGebra, which you can do, too, of course.

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08-30-2019
06:25 AM

08-30-2019
06:25 AM

Re: Best solution in Mathcad needed!

Who said that point P must be inside the quadrangle!

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08-30-2019
10:45 AM

08-30-2019
10:45 AM

Re: Best solution in Mathcad needed!

@ValeryOchkov wrote:

Who said that point P must be inside the quadrangle!

You didn't say anything at all when you "asked" - that was the problem with your question from the very first post you made. You just showed a picture where we could read "Find AP = x-?" Not AP with a straight line/bar over it, so we even can't say if the length of a line segment is meant or something else. We also don't know what the minus sign after x should mean - are you looking for the subtrahend of a difference? Luc noted the "missing" right angles resp. missin lengths which you later submitted.

So what could we do with that initial post of yours? As I see it we had just two options: assume the most obvious or reject the question as inadequate. Maybe the second variant would have been more appropriate?

Anyway, I look forward for you to show us correct symbolic solutions and of course an animation showing all possible solutions 😉