Don't Understand Solution 5

[treddie]

Howdie.
I must confess ignorance of this solution (please see attached). I know my trig, geom, some calculus and linear algebra, but this solution is getting into unknown territory for me. Can anybody tell me what form of math this is, or is it just typical math wrapped in cryptic MathCAD syntax? It looks like it's saying something like,
"Take 2 * arctangent of a new variable (_z) only if (_z) is an element of the root of blah, blah, blah." If that is true, that is certainly easy enough to understand, but what the heck is (X721)?!
Thanks in advance,
treddie

 

[treddie]

I forgot to mention that the orignal equation was being solved for (THETA1_prime). But with (X721) in there, it appears that the solution is not explicit, which would be a bummer in this case.
treddie

 

[treddie]

GEEZ! I meant, (THETA1_2prime).

 

[Dinosaur]

I have never seen a solution expressed this way; however, it appears to me you have the correct interpretation. Good Luck.

 

[miecz]

It looks as though X721 is simply a variable (with an odd name) defined earlier in the worksheet.

 

[PNachtwey]

I would post this on sci.math.symbolic.
You don't say what you are solving for.
I often get answers that are in terms of RootOf( a polynomial of _Z ).
In this case I must solve for _Z symbolically or numerically and then substitute the answer for the RootOf(_Z) expression. I think your case is similar except you must solve for X721 and _z can be any one of the roots. What is curious is the ,X721 at the end. I doubt you will a symbolic answer but that is why I suggest posting this on the sci.math.symbolic use group. There are some very good mathematicians there and some have Mathematica and Maple and may solve this for you.

 

[treddie]

Thank you for the replies.

miecz > Sorry. The solution was for (THETA1_2prime). (X721) is not defined earlier which makes the result frustrating.

PNachtwey > I am afraid you are correct. Unfortunately, I was REALLY hoping I would get back an analytical solution becuase that solution needs to go inside a ProEngineer Relation (which does not allow programming principles like FOR/NEXT, IF/ELSEIF, GOTO, etc. Go figure). I will pass this question on to sci.math.symbolic per your suggestion.

 

[IRstuff]

You might see if someone at work has Mathematica, Maple, or MuPad. Mathcad14 uses a subset of MuPad. Both Mathematica and Maple are probably substantially more capable than Mathcad at doing symbolic solutions.

However, given form of the given equation, it's probably unlikely to yield a closed-form solution.

TTFN

FAQ731-376

 

[treddie]

Dinosaur > Yah, this was the first time I've come across a solution that looks this way, too.

IRstuff > I may want to look at giving one of those apps a try, not just for this particular problem, but for general use altogether. MathCAD seems like it has a lot of operational "holes" in it. Not always particularly user-friendly.

 

[jghrist]

I tried to solve using Mathcad 13, but it didn't find a solution. It also didn't give any X721 variables.

 

[treddie]

Thanks for trying there, jghrist. Definitely a weird solution. Weird also in that MathCAD introduces this new variable (X721) with no clarification on how that variable is to be used or even what it means. And their docs are only semi-helpful. Is it an integer coefficient, a real number, complex number or one of Zarda from the planet Zakaroonda's famous equations? Or something else?

 

[philipoakley]

A quick response to the text (rather than the worksheet)

This is one of the 'new' features that the new MuPad symbolic engine has introduced. It is slightly more pedantic about solutions, including complex numbers being an option and trig functions repeating on 2pi etc.

These extra variables beginning with an underscore are a way of allowing those multiple solutions to happen. For particular types of solutions there are a set of default variables that are used. They are "hidden" in the tutorials and quicksheets. It would be 'normal' to substitute the default result for a variable of your choosing after its first showing.

 

[treddie]

philipoakley,
Is there some good documentation on this other than the tutorials and quicksheets? It's such a drag going through a zillion tuts and qsheets to find the ones that apply, and dig out what's going on. If not, I'll just dig in and go for it.
treddie