NEED URGENT HELP! Code keeps returning the desired variables as empty 0x1

My code is currently only returning Empty sym: 0-by-1.

CODE:

clear;

clc;

%Knowns

%Knowns

i = sqrt(-1);

Theta_AB = 0;

Theta_DB = 90*(pi/180);

Omega_AB = 0;

Alpha_AB = 0;

Omega_AC = 15*(360/1)*(pi/180)*(1/60);

R_AB = 24;

syms R_AC R_CD R_DB R_EB Theta_AC Theta_CD Omega_CD Omega_DB Alpha_AC Alpha_CD Alpha_DB

%Real

EqnRP1 = R_AC*cos(Theta_AC) + R_CD*cos(Theta_CD) + R_DB*cos(Theta_DB) - R_AB*cos(Theta_AB) == 0;

EqnRV1 = R_AC*Omega_AC*(-sin(i*Theta_AC)) + R_CD*Omega_CD*(-sin(Theta_CD)) + R_DB*Omega_DB*(-sin(Theta_DB)) - R_AB*Omega_AB*(-sin(Theta_AB)) == 0;

EqnRA1 = R_AC*Omega_AC^2*(-cos(Theta_AC)) + R_AC*Alpha_AC*(-sin(Theta_AC)) + R_CD*Omega_CD^2*(-cos(Theta_CD)) + R_CD*Alpha_CD*(-sin(Theta_CD)) + R_DB*Omega_DB^2*(-cos(Theta_DB)) + R_DB*Alpha_CD*(-sin(Theta_DB)) - R_AB*Omega_AB^2*(-cos(Theta_AB)) - R_AB*Alpha_CD*(-sin(Theta_AB)) == 0;

%Imagininary

EqnIP1 = R_AC*i*sin(Theta_AC) + R_CD*i*sin(Theta_CD) + R_DB*i*sin(Theta_DB) - R_AB*i*sin(Theta_AB) == 0;

EqnIV1 = R_AC*Omega_AC*i*cos(Theta_AC) + R_CD*Omega_CD*i*cos(Theta_CD) + R_DB*Omega_DB*cos(Theta_DB) - R_AB*Omega_AB*cos(Theta_AB) == 0;

EqnIA1 = R_AC*Omega_AC^2*i*(cos(Theta_AC)) + R_AC*Alpha_AC*i*(-sin(Theta_AC)) + R_CD*Omega_CD^2*i*(cos(Theta_CD)) + R_CD*Alpha_CD*i*(-sin(Theta_CD)) + R_DB*Omega_DB^2*i*(cos(Theta_DB)) + R_DB*Alpha_CD*i*(-sin(Theta_DB)) - R_AB*Omega_AB^2*i*(cos(Theta_AB)) - R_AB*Alpha_CD*i*(-sin(Theta_AB)) == 0;

%Additional Constraints

Eqn1 = Theta_AC == Theta_CD;

Eqn2 = 739.2 == Omega_DB*R_EB;

Eqn3 = R_AC + R_EB <= R_CD + R_AB;

Eqn4 = Alpha_DB * R_EB <= 3;

Eqn5 = R_EB <= R_AB + 6;

[R_AC, R_CD, R_DB, R_EB, Theta_AC, Theta_CD, Omega_CD, Omega_DB, Alpha_AC, Alpha_CD, Alpha_DB] = vpasolve([EqnRP1, EqnRV1, EqnRA1, EqnIP1, EqnIV1, EqnIA1, Eqn1, Eqn2, Eqn3, Eqn4, Eqn5],[R_AC, R_CD, R_DB, R_EB, Theta_AC, Theta_CD, Omega_CD, Omega_DB, Alpha_AC, Alpha_CD, Alpha_DB]);

R_AC

R_CD

R_EB

COMMAND WINDOW:

R_AC =

Empty sym: 0-by-1

R_CD =

Empty sym: 0-by-1

R_EB =

Empty sym: 0-by-1

>>

Answer 1

[John D'Errico]

Must a solution exist for all problems? No. Of course not. Those empty syms are a signal that MATLAB was unable to solve your problem. That does not mean there is no solution. Just that one could not be found.

The fact is however, that while it LOOKs like you have 11 equations, some of them are inequalities. And that means that there MAY be infinitely many solutions. But this is a very complicated system. So hoping for some explicit solution is way too optimistic.

[Michael]

Okay. Do you think there is anyway to change the parameters to get a solution? I have tried several changes to Eqn4, Eqn5, and Omega_AC? This is for a design project.

[Michael]

If I change the inequalities to a definite answer, do you think that it may help? I have run systems like this before and gotten definite answers.