I have this system of four nonlinear equations:
the unknowns are a1, a2, gamma1 and gamma 2. all other parameters are known. What I want is to plot the a1 vs sigma2 as below:
I tried findinstance
but it takes a lot of time to find the results for any value of sigma2, Let alone plotting a1 for different values of sigma2!
Can anybody help me?
Thanks in advance
Here are the codes for the four equations and the corresponding values for the parameters:
8*Subscript[\[Omega], 1]*Subscript[\[Mu], 1]*Subscript[a, 1] -
Subscript[\[Alpha], 2]*Subscript[a, 1]^2*Subscript[a, 2]*
Sin[Subscript[\[Gamma], 1]] -
4*Subscript[f, 1]*Sin[Subscript[\[Gamma], 2]] == 0;
8*Subscript[\[Omega], 2]*Subscript[\[Mu], 2]*Subscript[a, 2] +
Subscript[\[Alpha], 5]*Subscript[a, 1]^3*
Sin[Subscript[\[Gamma], 1]] == 0;
8*Subscript[\[Omega], 1]*Subscript[a, 1]*
Subscript[\[Sigma],
2] + (3*Subscript[\[Alpha], 1]*Subscript[a, 1]^2 +
2*Subscript[\[Alpha], 3]*Subscript[a, 2]^2)*Subscript[a, 1] +
Subscript[\[Alpha], 2]*Subscript[a, 1]^2*Subscript[a, 2]*
Cos[Subscript[\[Gamma], 1]] +
4*Subscript[f, 1]*Cos[Subscript[\[Gamma], 2]] == 0;
8*Subscript[\[Omega], 2]*
Subscript[a,
2]*(3*Subscript[\[Sigma], 2] -
Subscript[\[Sigma], 1]) + (3*Subscript[\[Alpha], 8]*
Subscript[a, 2]^2 +
2*Subscript[\[Alpha], 6]*Subscript[a, 1]^2)*Subscript[a, 2] +
Subscript[\[Alpha], 5]*Subscript[a, 1]^3*
Cos[Subscript[\[Gamma], 1]] == 0;
Also the values for the parameters are:
Subscript[\[Omega], 1] = 10;
Subscript[\[Mu], 1] = 1;
Subscript[\[Alpha], 2] = -66.319;
Subscript[f, 1] = 1;
Subscript[\[Omega], 2] = 30;
Subscript[\[Mu], 2] = 1;
Subscript[\[Alpha], 5] = -3.6;
Subscript[\[Alpha], 1] = -24.85;
Subscript[\[Alpha], 3] = -9.2;
Subscript[\[Alpha], 6] = -66.3;
Subscript[\[Alpha], 8] = -345;
Subscript[\[Sigma], 1] = 0.08;
f1 = 0;
Markdown help
$\endgroup$ – Bob Hanlon Jul 23 '17 at 16:54Solve
to obtain expressions for theSin
s of the two gammas in the first two equations, and then of theCos
s off the same quantities from the last two equations. Square the respective results and add to eliminate the two gammas, leaving two polynomials in in alpha1 and alpha2. Then, useSolve
again to obtain expressions for them, which can be plotted usingPlot
. $\endgroup$ – bbgodfrey Jul 23 '17 at 19:31