How to solve equations in variable terms?

Question

yehuda kristo 2023-4-21

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1950878-how-to-solve-equations-in-variable-terms

评论： yehuda kristo 2023-4-21

I wanted to find equation solving a, b, c, and d in terms of e, f, g, and h. Is it possible to do this in MATLAB? Here's my code for the moment.

clc

clear all

syms a b c d e f g h alpha

A = [a b; c d];

R = [cos(alpha) -sin(alpha); sin(alpha) cos(alpha)];

D = (R*A)*transpose(R);

e=D(1,1)

e =

f=D(1,2)

f =

g=D(2,1)

g =

h=D(2,2)

h =

eqn=[e f g h];

solver=solve(eqn,[a b c d])

solver = struct with fields:

a: 0 b: 0 c: 0 d: 0

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Answer 1

Dyuman Joshi 2023-4-21

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https://ww2.mathworks.cn/matlabcentral/answers/1950878-how-to-solve-equations-in-variable-terms#answer_1220253

在 MATLAB Online 中打开

syms a b c d e f g h alpha
A = [a b; c d];
R = [cos(alpha) -sin(alpha); sin(alpha) cos(alpha)];
D = (R*A)*transpose(R);
%Modify the equations
eq1 = e-D(1,1)==0;
eq2 = f-D(1,2)==0;
eq3 = g-D(2,1)==0;
eq4 = h-D(2,2)==0;
eqn=[eq1 eq2 eq3 eq4];
solver=solve(eqn,[a b c d])
solver = struct with fields:
    a: (e*cos(alpha)^2 + h*sin(alpha)^2 + f*cos(alpha)*sin(alpha) + g*cos(alpha)*sin(alpha))/(cos(alpha)^2 + sin(alpha)^2)^2
    b: (f*cos(alpha)^2 - g*sin(alpha)^2 - e*cos(alpha)*sin(alpha) + h*cos(alpha)*sin(alpha))/(cos(alpha)^2 + sin(alpha)^2)^2
    c: (g*cos(alpha)^2 - f*sin(alpha)^2 - e*cos(alpha)*sin(alpha) + h*cos(alpha)*sin(alpha))/(cos(alpha)^2 + sin(alpha)^2)^2
    d: (h*cos(alpha)^2 + e*sin(alpha)^2 - f*cos(alpha)*sin(alpha) - g*cos(alpha)*sin(alpha))/(cos(alpha)^4 + sin(alpha)^4 + 2*cos(alpha)^2*sin(alpha)^2)