Has anyone seen this form of a nonlinear equation with respect to X, but linear with respect to Y & Z? I provided a contour plot within the region for all 3 variables between -2 & 2. The plot is actually Z*conjugate(Z) so that the magnitude is above ZERO. If I am correct I may have seen this before in orbital mechanics, but my undergrad years are a bit behind me. I generated this eq. during a parametric analysis of a 2nd order oscillator. I would like to come up to speed about the physical phenomena this equation might describe.
I would provide a PDF of my results, but I do not see that I can upload a file. So below is my MATLAB code. If you can provide info how to attach or upload a file please respond.
alpha=-2:0.004:2; rho=10^-6; for k=1:length(alpha)-1 rho(k+1)=rho(k)*10^(12/(length(alpha)-1)); end ones(1:k+1)=1; X=fliplr(-1*ones'*rho); X=[X ones'*rho]; Y=alpha'*ones; Y=[Y Y]; z=((1-Y).*((1-Y).^2+1).*((1+Y).^2-1).^2.*X-(1+Y).*((1+Y).^2+1).*((1-Y).^2-1).^2)./(4*(1-Y).*(1+Y).*((1-Y).*(1+(1+Y).^2)-(1+Y).*((1-Y).^2+1).*X)); Z=z.*conj(z); mesh(X,Y,Z); [m n]=size(Z); axis([X(1,1) X(m,n) Y(1,1) Y(m,n) 0 2 0 2])
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