Math Help - Need some Help with MathCad :)

1. Need some Help with MathCad :)

Hey all, Just wondering if anyone uses mathcad prime 1.0?

I'm using it at the moment and trying to find the co-efficients of an 8th order polynomial using boundary conditions.

if anyone can help me set up and solve this equation it would be much appreciated!

Thanks!

Here is the equation:

(@EQ (@LABEL VARIABLE L) (+ (+ (+ (+ (+ (+ (+ (+ (* (@LABEL VARIABLE A) (^ θ 8)) (* B (^ θ 7))) (* C (^ θ 6))) (* D (^ θ 5))) (* E (^ θ 4))) (* F (^ θ 3))) (* G (^ θ 2))) (* H θ)) I))

Ok cant just copy paste I see!

$L= A* x^8+ B* x^7+C* x^6+D* x^5+E* x^4+F* x^3+G* x^2+H* x+I$

2. Re: Need some Help with MathCad :)

Are the various values of $x$ randomly spaced or are they evenly spaced ? What do you mean by boundary condotions in this context ?

3. Re: Need some Help with MathCad :)

I have only 3 boundary conditions:

if x= 90 then L= 11.5, if x=45 then L=11.5/2 if L=0 then x=0

As for how the constants are spaced I have no idea.
x is actually theta but I couldnt find that here. x is an angle

Its for a Cam design project

4. Re: Need some Help with MathCad :)

You have nine unknown coefficients, that means that you need nine pairs of values for $L$ and $x$ to determine all of them uniquely.

5. Re: Need some Help with MathCad :)

No other way at all?

6. Re: Need some Help with MathCad :)

Guess some inbetween Ls and x's?

7. Re: Need some Help with MathCad :)

You could do if that is acceptable to your design. Can you make use of symmetry in some way ? Is it symmetrical about some axis ? If you do manage to generate some more points, calculations are easier if the $x$ values are equally spaced. BTW, I know nothing about MathCad. What we are talking about is independent of MathCad (or any other calculating device).

8. Re: Need some Help with MathCad :)

Awesome, thanks Bob, I'm sure there is a way to do this I just don't know what I'm about really! Thanks for your help Bob- I will see if i can gather more info before I bother you guys again! Sorry about this.

9. Re: Need some Help with MathCad :)

With your specified 3 boundary values it is possible to eliminate 3 of coefficients and obtain the following result:

$L(x)=h x+g x^2+f x^3+e x^4+d x^5+c x^6+\left(\frac{2921}{95659380000000}-\frac{c}{30}-\frac{7 d}{8100}-\frac{e}{48600}-\frac{31 f}{65610000}-\frac{7 g}{656100000}-\frac{127 h}{531441000000}\right) x^7+\left(-\frac{161}{478296900000000}+\frac{c}{4050}+\frac{d }{121500}+\frac{7 e}{32805000}+\frac{f}{196830000}+\frac{31 g}{265720500000}+\frac{7 h}{2657205000000}\right) x^8$