Matrix terms are reversed when evaluated symbolically

[MI_10648350]

when evaluating frequency equation for a MDOF model, if the stiffness and mass matrices are defined in terms of mass, elasticity, and etc constants, the resulting terms of the symbolic evaluation are reversed. (see below). I know that the result in terms of the constants is the correct answer. However, I dont understand why the determinant using values only gives reversed terms? Any ideas or pointers are apprieciated.

Thanks 

[MI_10648350]

Here's a follow up. 

correction: Im not sure which is the correct answer. when solving the equation by hand the roots are as follows 

 which Im assuming the correct answer. Also the matrix terms are as expected 

 However, when solving it in terms of the constants EI,m,L. The terms are as follows 

 where 

WHY IS MATHCAD GIVING ME a DIFFERNT result than expected? 

[Werner_E · Accepted solution]

I see no problem here.

There is no rule or convention about the order in a set of multiple solutions to an equation.

Its quite possible that the symbolics returns the solutions in a different order depending on if just numbers are used or variables & units.

As we don't know how the symbolic "solve" is implemented internally we can't say why.

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WHY IS MATHCAD GIVING ME a DIFFERNT result than expected? 

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Mathcad gives you a correct result - it can't know what you expect 😉

[MI_10648350]

Thanks Wener_E! it seems logical. It was my initial thought, but what about the embedded matrices? I cant make sense of those extra terms?  

[Werner_E]

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@MI_10648350 wrote:

Thanks Wener_E! it seems logical. It was my initial thought, but what about the embedded matrices? I cant make sense of those extra terms?  

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Which extra terms?

Do you talk about the nested matrices when you evaluated the variable "w"?

You don't show how "w" was calculated, so I can't say anything about it.

BTW, apart from showing pictures you sure should attach the worksheet itself.

[MI_10648350]

Here is the worksheet. However, for some reason the nested matrices disappeared! not sure what happened, but its the same exact code I wrote earlier. Im still new to symbolic evals so I guess I have a lot to learn. 

[Werner_E]

Hard to say what cold have caused Prime to give you the nested matrices for "w".
Chances are that you had defined something differently from whats now in the sheet or that you deleted some definition you had.

It looks like you use a n older version of Prime (P6 or below) which uses the older symbolic muPad (which was in many respects more capable than the new one, an Axiom fork).

Here is what I see in Prime 9 when I recalculate the sheet.

As you can see its necessary to use "assume,ALL>0" to get a similar result as you got with muPad.

Actually the new symbolic is correct because sqrt(x^2)=x is only valid if x>=0. Generally sqrt(x^2)=|x|

BTW, you can always assign the result of the symbolic evaluation to a function instead of a variable and so can get the numeric results in the same order as the symbolic results:

And o fcourse because you use Mathcad/Prime you should take advantage of its strength and use units throughout.