Solving nonlinear equations using matrix
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I have
p11 X1 + p12 X2 + p13 X3 + (-sin(psi) cos(X5) cos(X6) + cos(psi) sin(X5)) X4 &= C_1 (i) ;
p21 X1 + p22 X2 + p23 X3 + (-(1 + sin^2(psi)) cos(X5) cos(X6) + sin(psi) cos(psi) sin(X5)) X4 &= C_2(i) ;
p31 X1 + p32 X2 + p33 X3 + (-cos(X5) sin(X6)) X4 &= C_3 (i) \
p41 X1 + p42 X2 + p43 X3 + (- cos(psi) sin (psi) cos(X5) cos(X6) + (1 + cos^2(psi)) sin(X5)) X4 &= C_4(i) ;
p51 X1 + p52 X2 + p53 X3 + (- (1 + q) sin (psi) cos(X5)cos(X6) + (1 + q)cos(psi) sin(X5)) X4 &= C_5 (i) ;
p61 X1 + p62 X2 + p63 X3 - cos(X5) cos(X6) X4 &= C_6 (i);
Here i = 1: 6, C_1(i), C_2(i) ..... etc., coefficients p11, p12, ..... p63 are the constants and q = constant, psi = constant. Need to solve the equations for X1, X2, X3, X4, X5, X6. I am new to code to solve tis kind of equations. I request any suggestions and help. Thanks!
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Kartik Saxena
am 21 Mär. 2024
Hi,
Based on your problem, I'm adding a sample code snippet to solve this kind of problems, you can refer to it in order to design your solution according to your problem:
syms X1 X2 X3 X4 X5 X6 psi q
p = sym('p', [6, 3]); % Define the coefficient matrix p
C = sym('C', [6, 1]); % Define the constant vector C
eq1 = p(1,1)*X1 + p(1,2)*X2 + p(1,3)*X3 + (-sin(psi)*cos(X5)*cos(X6) + cos(psi)*sin(X5))*X4 == C(1);
eq2 = p(2,1)*X1 + p(2,2)*X2 + p(2,3)*X3 + (-(1 + sin(psi)^2)*cos(X5)*cos(X6) + sin(psi)*cos(psi)*sin(X5))*X4 == C(2);
eq3 = p(3,1)*X1 + p(3,2)*X2 + p(3,3)*X3 + (-cos(X5)*sin(X6))*X4 == C(3);
eq4 = p(4,1)*X1 + p(4,2)*X2 + p(4,3)*X3 + (-cos(psi)*sin(psi)*cos(X5)*cos(X6) + (1 + cos(psi)^2)*sin(X5))*X4 == C(4);
eq5 = p(5,1)*X1 + p(5,2)*X2 + p(5,3)*X3 + (-(1 + q)*sin(psi)*cos(X5)*cos(X6) + (1 + q)*cos(psi)*sin(X5))*X4 == C(5);
eq6 = p(6,1)*X1 + p(6,2)*X2 + p(6,3)*X3 - cos(X5)*cos(X6)*X4 == C(6);
% Solve the equations
sol = solve([eq1, eq2, eq3, eq4, eq5, eq6], [X1, X2, X3, X4, X5, X6]);
% Display the solutions
sol.X1
sol.X2
sol.X3
sol.X4
sol.X5
sol.X6
Also, refer to the following MathWorks documentations:
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