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]);
  4 个评论
Andrea Cesaro
Andrea Cesaro 2023-7-17
Ok thank you, but although I add ro like an other unknown Matlab is not able to solve it
Andrea Cesaro
Andrea Cesaro 2023-7-17
Like this:
clc
clear
close all
syms phi1
syms theta1
syms phi2
syms theta2
syms phi3
syms theta3
syms phi4
syms theta4
syms ro
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, ro] = solve(eqns, [phi1, theta1, phi2, theta2, phi3, theta3, phi4, theta4, ro]);

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采纳的回答

Dheeraj
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,
  1. Simplifying the equations or by breaking down the problem to subproblems and solve them separately and try to combine the results at the end.
  2. 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

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