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yhuang-31-Visitor
1-Visitor
October 9, 2015
Solved

Would someone help me in finding out how to solve an equation

  • October 9, 2015
  • 2 replies
  • 6191 views

Hi all, I want to use symbolic solver to convert a fourth order equation to the multiplication of two second order terms. All variables are real numbers. I defined the equation like this but Mathcad showed no solution for it.

mathcad derivation.png

I attached the complete source code of Mathcad here. A big portion of this worksheet is the derivation of the left hand side of the equation, so you can simply ignore it (unless some of them are not executed by mathcad successfully). Would someone advise what is wrong with my solution? Can I put more restrictions in Mathcad, such as assume k0,k are real, to figure this out?


Many thanks!

Best answer by AlvaroDíaz

Don´t know if is useful, but this is the numeric solution. Obviously, must to make good guess for each alpha.q.gif

2 replies

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RichardJ19-Tanzanite
19-Tanzanite
October 9, 2015

You can greatly simplify the equations you are trying to solve. See the attached. Also note that you have no multiplication operator between k0 and the left parenthesis, which makes k0 a function name. I assume that's a mistake.

Fixing the above will not help though. k^2 appears in the numerator and in the denominator, so you have a fourth order polynomial in k. There is no symbolic solution for that.

Y
yhuang-31-VisitorAuthor
1-Visitor
October 10, 2015

Hi Richard, thank you for your advise! I did find a mistake from my side in defining k0, but the existing of it is correct. I am trying to solve alpha*s^4=s^4/(k0^2*wn1^4).

Do you think putting any limitation will help in solving this problem? For example. can I define k is much larger than 1? In control system, to separate two poles, we generally want to separate k*wn1 and wn1/k in frequency domain. Would you suggest can I do it? Thank you!

R
RichardJ19-Tanzanite
19-Tanzanite
October 10, 2015

Well, I made a mistake too. I made some changes, and forgot to put the variables back on the left hand side of the equations. Here's an update. It doesn't change the conclusion though.

Hi Richard, thank you for your advise! I did find a mistake from my side in defining k0, but the existing of it is correct. I am trying to solve alpha*s^4=s^4/(k0^2*wn1^4).

Do you think putting any limitation will help in solving this problem? For example. can I define k is much larger than 1? In control system, to separate two poles, we generally want to separate k*wn1 and wn1/k in frequency domain. Would you suggest can I do it? Thank you!

I'm not sure I quite understand your corrected equation, since you have s^4 on both sides, which will just cancel.

Regardless, there is no symbolic solution for a fourth order polynomial. Why do you need to solve this symbolically? Finding the solution numerically is almost certainly possible, and much easier.

L
LucMeekes23-Emerald IV
23-Emerald IV
October 10, 2015

So what you want is:

And now you want to express k0, k, Q5 and Q6 (and NOT wn1...!)  in terms of the greek letters.

OK. Expansion of the right-hand-side gives:

for which we can find the coefficients:

and finally we find:

which means that to find k we have to solve an 8th order polynomial symbolically.

I guess that's a bit too much.

Luc

A
AlvaroDíaz12-Amethyst
12-Amethyst
October 13, 2015

Hi Yuhang. I can't get a solution with those assumptions.

q.gif

Y
yhuang-31-VisitorAuthor
1-Visitor
October 13, 2015

Hi Alvaro, thank you so much for your help! I am trying to follow your pattern to see what I can do in my original worksheet, but got the problem in putting the line after the ":=" equation (the one above the red texts in your picture).  Would you advise me how to can use "Add line" command to put it after the Q():=Im(Phai()) ?

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