what's the relation between A , B and M,G for this Nonlinear system of equation ?

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YOUSSEF El MOUSSATI 2024-2-11

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评论： YOUSSEF El MOUSSATI 2024-2-11

采纳的回答： Torsten

A*sin(3*Phi)-B*sin(Phi) = G ;

A*cos(3*Phi)-B*cos(Phi) = M ;

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Torsten 2024-2-11

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A^2 + B^2 - 2*A*B*cos(2*Phi) = G^2 + M^2

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Torsten 2024-2-11

编辑：Torsten 2024-2-11

在 MATLAB Online 中打开

If each of the equations could be solved uniquely for Phi, you could get what you want.

Assume that the first equation would uniquely yield Phi = f(A,B,G) and the second equation would uniquely yield Phi = g(A,B,M), then f(A,B,G) - g(A,B,M) = 0 would be your relation. But unfortunately, the equations cannot be solved uniquely for Phi.

syms A B G M Phi

eqn = A*sin(3*Phi)-B*sin(Phi) == G ;

sol1 = solve(eqn,Phi,'ReturnConditions',1,'MaxDegree',3)

sol1 = struct with fields:

Phi: [6×1 sym] parameters: k conditions: [6×1 sym]

sol1.Phi

ans =

sol1.conditions

ans =

YOUSSEF El MOUSSATI 2024-2-11

Ok , thanks for your help , it's very important to me

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John D'Errico 2024-2-11

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编辑：John D'Errico 2024-2-11

This is not even remotely a question about MATLAB. As such, it should arguably not even be on Answers. But I have a minute to respond, so I will choose to do so.

Trivial! What is the relation? Admittedly, the relation itself is a slightly complex thing, composed of two equations. The relations are:

A*sin(3*Phi)-B*sin(Phi) = G

A*cos(3*Phi)-B*cos(Phi) = M

which is exactly what you wrote.

It is not a nonlinear system of equations though. Not at all! Phi there is simply a parameter, not one of the parameters involved. That makes your problem fully a LINEAR system of equations. As such, if you want to view it in that form, then we could write:

M = [sin(3*Phi), -sin(Phi); ..

cos(3*Phi), -cos(Phi)]

So M is a matrix function of the parameter Phi. Biven the matrix M, then we could write:

M*[A;B] = [G;M]

There is no simpler relation between those variables. And it is NOT at all nonlinear. Purely linear.

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YOUSSEF El MOUSSATI 2024-2-11

Ok ,thanks for your answer , yes this system is linear but the parameters A,B and C,D are Nonlinear A=f(x^3,x^2,x); B=g(x^3,x^2,x); C=h(x^3,x^2,x); D=l(x^3,x^2,x);

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