Assisted Simplification with other equations?

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Ali Almakhmari
Ali Almakhmari 2023-10-10
评论： Ali Almakhmari 2023-10-11
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;

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采纳的回答

Torsten
Torsten 2023-10-10
移动：Walter Roberson 2023-10-11
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.
  1 个评论
Walter Roberson
Walter Roberson 2023-10-11
... 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.

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更多回答（1 个）

Sulaymon Eshkabilov
Sulaymon Eshkabilov 2023-10-10
Ran in:
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 = 
  2 个评论
Walter Roberson
Walter Roberson 2023-10-11
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
Ali Almakhmari 2023-10-11
Thank you both, I realized my mistake in the original expression and this command definitely will work for me.

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