How to solve symbolic system of non linear equation

Hi,

I need for a robotic project to solve (symbolic) the following system (express t2,t3,t4 in function of x y z) i've created this script but it's not working at all

syms t2 real;
syms t3 real;
syms t4 real;
syms x;syms y;syms z;
eq1=335*cos(t2)* sin(t3) -77*sin(t2)-260*sin(t2)*sin(t4)+260*cos(t2)*cos(t3)*cos(t4)+85==x;
eq2=335*cos(t3)-260* sin(t3)*cos(t4)==y;
eq3=0-335*sin(t2)* sin(t3) -77*cos(t2) -260*cos(t2)*sin(t4)-260*sin(t2)*cos(t3)*cos(t4) ==z;
[solt1,solt2,solt3]=solve(eq1,eq2,eq3,x,y,z)

solt1 = 

solt2 = 

solt3 = 

Answer 1

[Torsten]

[solt1,solt2,solt3]=solve(eq1,eq2,eq3,t2,t3,t4);

Best wishes

Torsten.

[ves dim]

thanks torsten but there is an error message : error in solve (line8)

[Torsten]

This simple example works ?

syms u v
eqn1 = 2*u^2 + v^2 == 0;
eqn2 = u - v == 1;
sol = solve(eqn1,eqn2,u,v);
sol.u
sol.v

If not, your MATLAB version is too old for this syntax and you will have to consult the documentation on how to call "solve" for your earlier version.

Best wishes

Torsten.

[ves dim]

I have a 2015 version matlab. But I think the problem is more complex than your example indeed my system is a non linear system, and i think that there is a specific way to write it in matlab

[Torsten]

But it says: error. That means something with your syntax is incorrect. It does not mean that MATLAB con't find a solution.

So the above simple example works in your case ? If yes, then what's the complete error message if you use

syms x y z t2 t3 t4
eq1 = 335*cos(t2)*sin(t3)-77*sin(t2)-260*sin(t2)*sin(t4)+260*cos(t2)*cos(t3)*cos(t4)+85==x;
eq2 = 335*cos(t3)-260*sin(t3)*cos(t4)==y;
eq3 = -335*sin(t2)*sin(t3)-77*cos(t2)-260*cos(t2)*sin(t4)-260*sin(t2)*cos(t3)*cos(t4)==z;
[solt2,solt3,solt4]=solve(eq1,eq2,eq3,t2,t3,t4);

Best wishes

Torsten.

[Steven Lord]

What is the FULL, EXACT text of the error message?

[ves dim]

indeed your script is not working on my computer i check solve documentation and i come back

[Walter Roberson]

In older versions of the toolbox, you need to code

A == B

as

(A) - (B)

However, by R2015a the "==" version should be supported, unless you happen to be using Maple for your symbolic engine instead of the Mathworks Symbolic Toolbox (if you did not install Maple then this does not apply to you.)

Answer 2

[rami a.sh]

As explained and written by you , there are 6 unknowns and 3 equations.

This system of equations cant be solved. So , x ,y, and z values should be defined before

as example:

syms t2 t3 t4
x=1;
y=;
z=7;
eq1 = 335*cos(t2)*sin(t3)-77*sin(t2)-260*sin(t2)*sin(t4)+260*cos(t2)*cos(t3)*cos(t4)+85==x;
eq2 = 335*cos(t3)-260*sin(t3)*cos(t4)==y;
eq3 = -335*sin(t2)*sin(t3)-77*cos(t2)-260*cos(t2)*sin(t4)-260*sin(t2)*cos(t3)*cos(t4)==z;
[solt2,solt3,solt4]=solve(eq1,eq2,eq3,t2,t3,t4);

[Ezio Cosatto]

I've 13 unknowns and 13 equations, but I cannot solve the problem:

syms EBp EF FBp GCp GH HCp IDp IL LDp MAp MN NAp x real;
eqn1 = MAp*NAp/2==x;
eqn2 = NAp*EBp == MAp*FBp;
eqn3 = MAp*EF == MN*EBp;
eqn4 = EF*GCp == EBp*GH;
eqn5 = FBp*GH == EF*HCp;
eqn6 = GH*IDp == GCp*IL;
eqn7 = GH*LDp == HCp*IL;
eqn8 = IL*MAp == IDp*MN;
eqn9 = IL*NAp == LDp*MN;
eqn10 = EBp*FBp == 4;
eqn11 = GCp*HCp == 8;
eqn12 = LDp*IDp == 2;
eqn13 = GCp^2 + HCp^2 == GH^2;
[solu] = solve(eqn1,eqn2,eqn3,eqn4,eqn5,eqn6,eqn7,eqn8,eqn9,eqn10,eqn11,eqn12,eqn13,x)

 
solu =
 
Empty sym: 0-by-1
 

[Walter Roberson]

What you were requesting to do was find a single variable, x, that solved all 13 equations simultaneously. You need to solve() for as many variables as you have equations.

syms EBp EF FBp GCp GH HCp IDp IL LDp MAp MN NAp x real;
eqn1 = MAp*NAp/2==x;
eqn2 = NAp*EBp == MAp*FBp;
eqn3 = MAp*EF == MN*EBp;
eqn4 = EF*GCp == EBp*GH;
eqn5 = FBp*GH == EF*HCp;
eqn6 = GH*IDp == GCp*IL;
eqn7 = GH*LDp == HCp*IL;
eqn8 = IL*MAp == IDp*MN;
eqn9 = IL*NAp == LDp*MN;
eqn10 = EBp*FBp == 4;
eqn11 = GCp*HCp == 8;
eqn12 = LDp*IDp == 2;
eqn13 = GCp^2 + HCp^2 == GH^2;
[solu] = solve(eqn1,eqn2,eqn3,eqn4,eqn5,eqn6,eqn7,eqn8,eqn9,eqn10,eqn11,eqn12,eqn13)

solu = struct with fields:
    EBp: [24x1 sym]
     EF: [24x1 sym]
    FBp: [24x1 sym]
    GCp: [24x1 sym]
     GH: [24x1 sym]
    HCp: [24x1 sym]
    IDp: [24x1 sym]
     IL: [24x1 sym]
    LDp: [24x1 sym]
    MAp: [24x1 sym]
     MN: [24x1 sym]
    NAp: [24x1 sym]
      x: [24x1 sym]

solu.EBp

ans = 

solu.EF

ans =