# Assisted Simplification with other equations?

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Ali Almakhmari on 10 Oct 2023
Commented: Ali Almakhmari on 11 Oct 2023
I want to simplify an equation knowing certain other information. My equation is this:
syms b Q e gamma K_phi eta K_theta ao CL_delta delta_o CM_delta c ao
eqn = (ao*((CL_delta*Q)/ao - (Q^2*e*(tan(eta)*((CL_delta/ao + (CM_delta*c)/(ao*e))*((Q*b)/2 - cos(gamma)*sin(gamma)*(K_phi - K_theta)) + (CL_delta*b*(K_theta*cos(gamma)^2 - Q*e + K_phi*sin(gamma)^2))/(2*ao*e)) - (CL_delta/ao + (CM_delta*c)/(ao*e))*(K_phi*cos(gamma)^2 + K_theta*sin(gamma)^2 + (Q*b*tan(eta))/2) + (CL_delta*b*(cos(gamma)*sin(gamma)*(K_phi - K_theta) + Q*e*tan(eta)))/(2*ao*e)))/((K_phi*cos(gamma)^2 + K_theta*sin(gamma)^2 + (Q*b*tan(eta))/2)*(K_theta*cos(gamma)^2 - Q*e + K_phi*sin(gamma)^2) + (cos(gamma)*sin(gamma)*(K_phi - K_theta) + Q*e*tan(eta))*((Q*b)/2 - cos(gamma)*sin(gamma)*(K_phi - K_theta)))))/(CL_delta*Q);
I was told that using the below information that I can simplify eqn to be truely a function of gamma alone, but I cannot prove it or do it in MATLAB. The info is:
b/c = 6;
e/c = 0.1;
K_phi/K_theta = 3;
CL_delta/ao = 0.4805020381;
CM_delta/ao = -0.096610459;
eta = pi/6;

Torsten on 10 Oct 2023
Moved: Walter Roberson on 11 Oct 2023
I was told that using the below information that I can simplify eqn to be truely a function of gamma alone
Since Q does not appear in your 6 conditions, this cannot be true.
Walter Roberson on 11 Oct 2023
... Unless Q happens to appear in a way that cancels once you do the other substitutions. Which does not happen to be the case. The Q^2 in the numerator can be divided by the Q in the denominator, but that is going to leave a Q.

Sulaymon Eshkabilov on 10 Oct 2023
Use subs() command and assign variables properly, e.g.:
syms b Q e gamma K_phi eta K_theta ao CL_delta delta_o CM_delta c ao
eqn = (ao*((CL_delta*Q)/ao - (Q^2*e*(tan(eta)*((CL_delta/ao + (CM_delta*c)/(ao*e))*((Q*b)/2 - cos(gamma)*sin(gamma)*(K_phi - K_theta)) + (CL_delta*b*(K_theta*cos(gamma)^2 - Q*e + K_phi*sin(gamma)^2))/(2*ao*e)) - (CL_delta/ao + (CM_delta*c)/(ao*e))*(K_phi*cos(gamma)^2 + K_theta*sin(gamma)^2 + (Q*b*tan(eta))/2) + (CL_delta*b*(cos(gamma)*sin(gamma)*(K_phi - K_theta) + Q*e*tan(eta)))/(2*ao*e)))/((K_phi*cos(gamma)^2 + K_theta*sin(gamma)^2 + (Q*b*tan(eta))/2)*(K_theta*cos(gamma)^2 - Q*e + K_phi*sin(gamma)^2) + (cos(gamma)*sin(gamma)*(K_phi - K_theta) + Q*e*tan(eta))*((Q*b)/2 - cos(gamma)*sin(gamma)*(K_phi - K_theta)))))/(CL_delta*Q);
display(eqn)
eqn =
b = 6*c;
e = 0.1*c;
K_phi = 3*K_theta;
CL_delta = 0.4805020381*ao;
CM_delta = -0.096610459*ao;
eta = pi/6;
eqn=subs(eqn, b);
eqn=subs(eqn, e);
eqn=subs(eqn, K_phi);
eqn=subs(eqn, CL_delta);
eqn=subs(eqn, CM_delta);
eqn=subs(eqn, eta);
FINAL_eqn = eqn;
display(FINAL_eqn)
FINAL_eqn =
Walter Roberson on 11 Oct 2023
This is not going to be able to transform to an expression in just gamma. This is not the correct solution to the question asked, and Torsten had the correct answer.
Ali Almakhmari on 11 Oct 2023
Thank you both, I realized my mistake in the original expression and this command definitely will work for me.

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