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How to find unknown variable in the below equation?

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Megha
Megha 2020년 9월 1일
댓글: Megha 2020년 9월 3일
I wish to solve the equation as shown below:
So, I made a new variable "A1" as coded below with i/p parameters.
r = 3.88;
Vau = 43;
theta_u = 71.8;
gamma = 5/3;
Vsu = 47.45;
syms Unu
A1 = double(solve(((Unu^2 - (r * Vau^2 *(cosd(theta_u))^2))^2) * (Unu^2 - ((2 * r * Vsu^2)/(r+1-gamma*(r-1)))) - ((r * (sind(theta_u)^2) * Unu^2 * Vau^2) *((2 * r - gamma * (r-1))*(Unu^2)/(r+1-gamma(r-1)) - r * Vau^2 * (cosd(theta_u))^2))))
A1 shows error like:
Subscript indices must either be real positive integers or logicals.
Error in IPS_P2 (line 333)
A1 = double(solve(((Unu^2 - (r * Vau^2 *(cosd(theta_u))^2))^2) * (Unu^2 - ((2 * r * Vsu^2)/(r+1-gamma*(r-1)))) - ((r * (sind(theta_u)^2) * Unu^2 * Vau^2) *((2 * r - gamma * (r-1))*(Unu^2)/(r+1-gamma(r-1)) - r * Vau^2 * (cosd(theta_u))^2))))
Can anyone please help me, if there is any error in coding equation?

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Alan Stevens
Alan Stevens 2020년 9월 1일
The equation is a cubic in Unu^2, so the following uses roots to find solutions:
r = 3.88;
Vau = 43;
theta_u = 71.8;
gamma = 5/3;
Vsu = 47.45;
A = r*Vau^2*cos(theta_u)^2;
B = 2*r*Vsu^2/(r+1-gamma*(r-1));
C = r*Vau^2*sin(theta_u)^2;
D = (2*r - gamma*(r-1))/(r+1 - gamma*(r - 1));
% Let x = Unu^2
% (x - A)^2*(x - B) - C*x*(D*x - A) = 0
% (x/A - 1)^2*(x/A - B/A) - C/A*(x/A)*(D*x/A - 1) = 0
% Let y = x/A
% (y^2 - 2y + 1)*(y - B/A) - D*C/A*y^2 + C/A*y = 0
% Expand and collect like terms to get:
% y^3 -(2 + B/A + D*C/A)y^2 + (1 + 2*B/A + C/A)y - B/A = 0
p = [1; -(2 + B/A + D*C/A); (1 + 2*B/A + C/A); -B/A];
y = roots(p);
x = A*y; % reconstruct x
Unu = sqrt(x); % reconstruct Unu
disp(y)
disp(x)
disp(Unu)
% Check (f should be zero)
f = polyval(p,y);
disp(f)
  댓글 수: 6
Alan Stevens
Alan Stevens 2020년 9월 3일
"solve" produces a symbolic solution, but not all equations have symbolic solutions. "roots" provides numerical solutions only. As John said (above) "roots" is faster and more efficient.
Megha
Megha 2020년 9월 3일
Great. Thank you so much

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