Root finder solver for cubic equation
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Jamie Al
on 8 Mar 2021
Answered: Walter Roberson
on 8 Mar 2021
I have the following cubic equation in beta, knowing gamma, theta and M1 how can I find the roots of beta using MATLAB?
for example, knowing the following:
M1 = 8:3:20;
gamma = 1.4;
theta = 8;
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Accepted Answer
Walter Roberson
on 8 Mar 2021
syms M1 gamma theta_degrees tanbeta_degrees
eqn = 1 + (gamma - 1)/2 * M1.^2 * tand(theta_degrees).*tanbeta_degrees.^3 + (1-M1.^2).*tanbeta_degrees.^2 + (1+(gamma+1)/2.*M1.^2);
solbeta = solve(eqn, tanbeta_degrees);
beta_degrees = atand(solbeta)
M1_ = 8:3:20;
gamma_ = 1.4;
theta_degrees_ = 8; %in degrees
beta_values = subs(beta_degrees, {M1, gamma, theta_degrees}, {M1_, gamma_, theta_degrees_})
beta_numeric = double(beta_values)
whos beta_numeric
Here, the different columns correspond to the different M1 values, and the different rows correspond to the different roots of the cubic. Results are in degrees.
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