Resolution of a system with sine and cosine terms
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I write a code like this, but the run continues indefinitely; it seems that Matlab is not able to solve this system. Is that really the case or am I wrong somewhere?
clc
clear
close all
syms phi1
syms theta1
syms phi2
syms theta2
syms phi3
syms theta3
syms phi4
syms theta4
ro = sqrt(3);
csi1 = ro*sin(phi1)*cos(theta1);
eta1 = ro*sin(phi1)*sin(theta1);
zeta1 = ro*cos(phi1);
csi2 = ro*sin(phi2)*cos(theta2);
eta2 = ro*sin(phi2)*sin(theta2);
zeta2 = ro*cos(phi2);
csi3 = ro*sin(phi3)*cos(theta3);
eta3 = ro*sin(phi3)*sin(theta3);
zeta3 = ro*cos(phi3);
csi4 = ro*sin(phi4)*cos(theta4);
eta4 = ro*sin(phi4)*sin(theta4);
zeta4 = ro*cos(phi4);
eqns = [csi1^2 + csi2^2 + csi3^2 + csi4^2 == 4, eta1^2 + eta2^2 + eta3^2 + eta4^2 == 4, zeta1^2 + zeta2^2 + zeta3^2 + zeta4^2 == 4, csi1*eta1 + csi2*eta2 + csi3*eta3 + csi4*eta4 == 0, eta1*zeta1 + eta2*zeta2 + eta3*zeta3 + eta4*zeta4 == 0, zeta1*csi1 + zeta2*csi2 + zeta3*csi3 + zeta4*csi4 == 0, csi1 + csi2 + csi3 + csi4 == 0, eta1 + eta2 + eta3 + eta4 == 0, zeta1 + zeta2 + zeta3 + zeta4 == 0,...
theta1>0, theta1<2*pi, phi1>0, phi1<pi, theta2>0, theta2<2*pi, phi2>0, phi2<pi, theta3>0, theta3<2*pi, phi3>0, phi3<pi, theta4>0, theta4<2*pi, phi4>0, phi4<pi];
[phi1, theta1, phi2, theta2, phi3, theta3, phi4, theta4] = solve(eqns, [phi1, theta1, phi2, theta2, phi3, theta3, phi4, theta4]);
采纳的回答
Dheeraj
2023-8-10
Hi,
If the script is running for a long time without producing results, it's possible that the symbolic solver is struggling to find a solution due to the complexity of the equations or the constraints. Few ways you could work around to solve the problem are,
- Simplifying the equations or by breaking down the problem to subproblems and solve them separately and try to combine the results at the end.
- Using MATLAB parallel computing toolbox to speed up calculations. You may refer to this document on parallel computing for better understanding. https://in.mathworks.com/help/parallel-computing/getting-started-with-parallel-computing-toolbox.html
2 个评论
John D'Errico
2023-8-10
Yes. Note also that inequalities are difficult things to handle, and there are MANY of them here.
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