# System of equation with Mathematica: HELP

1. Apr 15, 2010

### ilvreth

System of equations with Mathematica: HELP

Hi there. I am trying to solve a system of equations. I have written a mathematica code to solve this systems
Code (Text):

<< VectorAnalysis`
Kc > Ku > 0;
Kuz > 0;
SS = 2.5;
Hfz > 0;
Kc = 0.0144;
Ku = Kc/3;
Kuz = 5 Kc;
B = 0.1;
Hfz = 0.1157676*B;
S = {Sx, Sy, Sz};
Eh = Kc (Sx^2  Sy^2 + Sx^2  Sz^2 + Sy^2   Sz^2) + Kuz   Sz^2 - Ku  Sx  Sy + SS  Hfz Sz;
Heffx = D[Eh, Sx];
Heffy = D[Eh, Sy];
Heffz = D[Eh, Sz];
Heff = -{Heffx, Heffy, Heffz};
Cross[S, Heff];
Sx = Sin[\[Phi]] Sin[\[Theta]];
Sy = Cos[\[Phi]] Sin[\[Theta]];
Sz = Cos[\[Theta]];
eq = Cross[S, Heff] == 0;
Reduce[{eq && 0 <= \[Phi] <= 2 \[Pi] && 0 <= \[Theta] <= \[Pi]}, {\[Phi], \[Theta]}, Reals]

where B is the magnetic field in Tesla. When i have B=0 it finds solution (which is simple without mathematica). But when you put a magnetic field e.g. B=0.1 does not give a solution and the program is running anyway...

Is there any way to find solutions with a numerical method or something?
(The system of equations contains 3 equations and these are the 3 components of the vector S x Heff )

Last edited: Apr 15, 2010
2. Apr 15, 2010

### CompuChip

I managed to make a slight improvement.
I'll just give you the code

Code (Text):
eq = Cross[S, Heff] == {0, 0, 0} // Thread // FullSimplify
criteria[\[Phi]_, \[Theta]_] := \[Phi] \[Element]
Reals && \[Theta] \[Element] Reals && 0 <= \[Phi] <= 2 \[Pi] &&
0 <= \[Theta] < \[Pi]
Select[NSolve[eq, {\[Theta], \[Phi]}],
criteria[\[Phi] /. #, \[Theta] /. #] &]
If you get confused, just shout, ok?

3. Apr 15, 2010

### ilvreth

Thank you very much my friend! Thank you for you help!

4. Apr 19, 2010

### ilvreth

How this code could be written in MATLAB?