Assisted Simplification with other equations?

Question

Ali Almakhmari 2023-10-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2031744-assisted-simplification-with-other-equations

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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Answer 1

Torsten 2023-10-10

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https://ww2.mathworks.cn/matlabcentral/answers/2031744-assisted-simplification-with-other-equations#answer_1330369

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.

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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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Answer 2

Sulaymon Eshkabilov 2023-10-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2031744-assisted-simplification-with-other-equations#answer_1330309

在 MATLAB Online 中打开

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 =

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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 2023-10-11