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error message in solving symbolic equation???

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syms m_c0 j_L0 theta1 M m_c_gama j_L_gama j_L_theta1 m_c_theta2 _L_theta2
syms m_c_theta1 gama l theta2 k1
eqn1=m_c_theta1==(m_c0-1/M+1)*cos(theta1)+j_L0*sin(theta1)+1/M-1;
eqn2=j_L_theta1==(-m_c0+1/M-1)*sin(theta1)+j_L0*cos(theta1);
%eqn3=m_m_theta1==1;
%eqn3=j_Lm_theta1==j_Lm0+l*theta1;
eqn4=m_c_theta2==j_L_theta1*sin(theta2-theta1)+(m_c_theta1+1)*cos(theta2-theta1)-1;
eqn5=j_L_theta2==j_L_theta1*cos(theta2-theta1)-(m_c_theta1+1)*sin(theta2-theta1);
%m_m_theta2=1;
%qn6=j_Lm_theta2==j_Lm0+l*theta2;
eqn7=m_c_gama==(1/k1)*j_L_theta2*sin(k1*(gama-theta2))+m_c_theta2*cos(k1*(gama-theta2));
eqn8=j_L_gama==j_L_theta2*cos(k1*(gama-theta2))-k1*m_c_theta2*sin(k1*(gama-theta2));
%eqn9=j_Lm_gama==j_L_gama;
%m_m_gama=(-m_c_theta2*cos(k1*(gama-theta2))-(1/k1)*j_L_theta2*sin(k1*(gama-theta2)))/(1+l)
m_c_gama=-m_c0;
j_L_gama=-j_L0;
j_L_theta2=(theta2*l)/2;
j_L_gama=j_L_theta2-l*(gama-theta2);
%j_L_theta2=j_Lm_theta2;
%j_Lm0=-j_Lm_gama;
%j_L_gama=j_Lm_gama;
eqns = subs([eqn1, eqn2, eqn4, eqn5, eqn7, eqn8]);
sol = solve(eqns, m_c0, j_L0, m_c_theta1,j_L_theta1,m_c_theta2,j_L_theta2)
this is showing some errors like this:
Error using sym.getEqnsVars>checkVariables (line 92)
The second argument must be a vector of symbolic variables.
Error in sym.getEqnsVars (line 62)
checkVariables(vars);
Error in solve>getEqns (line 450)
[eqns, vars] = sym.getEqnsVars(argv{:});
Error in solve (line 225)
[eqns,vars,options] = getEqns(varargin{:});
Error in eqnsolve_highvolfullload (line 28)
sol = solve(eqns, m_c0, j_L0, m_c_theta1,j_L_theta1,m_c_theta2,j_L_theta2,theta1, theta2)
what should be done?
  4 Comments
Manuela Gräfe
Manuela Gräfe on 25 Apr 2017
Hello, umme mumtahina.
I wrote comments under many of your question. Please provide the final solutions! Don't just write "got it!!!". This is a public community and some other people are also interested in the final solutions!
Please contact me via personal message! Click my profile and then send me a message please.

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Accepted Answer

Walter Roberson
Walter Roberson on 17 Feb 2017
You defined a value
j_L_theta2=(gama*l)/2;
That makes j_L_theta2 no longer a simple variable. You cannot solve for it in
sol = solve(eqns, m_c0, j_L0, m_c_theta1,j_L_theta1,m_c_theta2,j_L_theta2)
and you need to remove it from the end of the parameter list.
That would leave you with 6 equations and with you requesting to solve only 5 unknowns. There will be no solution to that.
The variables you are not solving for are M, gama, k1, l, theta1, and theta2 . You should add one of those to the solve() parameter list to solve for it. If you add M or l or theta1 to the parameter list then you will get a solution. However if you add gama or k1 or theta2 then no solution will be found.
  22 Comments
Walter Roberson
Walter Roberson on 22 Mar 2017
syms m_c0 j_L0 theta1 M m_c_gama j_L_gama j_L_theta1 m_c_theta2 j_L_theta2
syms m_c_theta1 gama l theta2 k1
eqn1L = m_c_theta1;
eqn1R = (m_c0-1/M+1)*cos(theta1)+j_L0*sin(theta1)+1/M-1;
eqn1 = eqn1L - eqn1R;
eqn2L = j_L_theta1;
eqn2R = (-m_c0+1/M-1)*sin(theta1)+j_L0*cos(theta1);
eqn2 = eqn2L - eqn2R;
eqn4L = m_c_theta2;
eqn4R = j_L_theta1*sin(theta2-theta1)+(m_c_theta1+1)*cos(theta2-theta1)-1;
eqn4 = eqn4L - eqn4L;
eqn5L = j_L_theta2;
eqn5R = j_L_theta1*cos(theta2-theta1)-(m_c_theta1+1)*sin(theta2-theta1);
eqn5 = eqn5L - eqn5R;
eqn7L = m_c_gama;
eqn7R = (1/k1)*j_L_theta2*sin(k1*(gama-theta2))+m_c_theta2*cos(k1*(gama-theta2));
eqn7 = eqn7L - eqn7R;
eqn8L = j_L_gama;
eqn8R = j_L_theta2*cos(k1*(gama-theta2))-k1*m_c_theta2*sin(k1*(gama-theta2));
eqn8 = eqn8L - eqn8R;
m_c_gama = -m_c0;
j_L_gama = -j_L0;
j_L_theta2 = (gama*l)/2;
residue = eqn1.^2 + eqn2.^2 + eqn4.^2 + eqn5.^2 + eqn7.^2 + eqn8.^2;
eqn = simplify( subs(residue) );
vars = [M, gama, j_L0, j_L_theta1, k1, l, m_c0, m_c_theta1, m_c_theta2, theta1, theta2];
Fvec = matlabFunction(eqn, 'vars', {vars});
Farray = matlabFunction(eqn, 'vars', vars);
Now you can use Fvec or Farray with a minimizer, looking for values near 0 (which indicate that all of the individual equations are balanced.)
The best I have found so far is
[ M, gama, j_L0, j_L_theta1, k1, l, m_c0, m_c_theta1, m_c_theta2, theta1, theta2] =
[0.264651987992054916, 2.2050144528762562e-17, 2.27231700419163755e-17, 1.74881407157095661e-17, -2.60182412177158895, 1.46780465953763239, 2.99999999999965894, 2.99999999999965894, -2.99999999999965894, 2.36395222838333151e-17, 2.39658891354045945e-17]
with a residue of 7.20318529637006345e-46 -- which is well into numeric noise level.
The search range I used for the above best value was
lowerbound [-1 -eps -eps -eps -3 -3 -3 -3 -3 0 0]
upperbound [ 1 eps eps eps 3 3 3 3 3 2*pi 2*pi]
The -1 to +1, and -3 to +3 were arbitrary restrictions because I could see from my graphics that there was a wide range of values for which they generated very low residues, indicating that the exact range of those values barely mattered. The 0 to +2*pi are for theta1 and theta2, known to be angles. The -eps to +eps were effective 0s for variables that I could see from my graphics had very low residues at values arbitrarily close to 0 -- though it turns out that m_c0 being just a little less than 3.0 is important for the very low residue with the other combination of values.
M of exactly 0 leads to NaN, as does k1 of exactly 0.

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