Hello everyone,
Hore you are doing well.
I am using the symbolic toolbox in MATLAB R2021a. I am interested in the coefficient which multiplies a certain variable.
In order to extract that coefficient, i am using the function coeffs which returns a vector containing the coefficients from lower degree to the highest. The returned vector is 1x2. When i want the second term in the vector, it replaces the variiable with 2.
syms M Rot_mat Inertia_principal_spar Ixx_spar Iyy_spar q_su(t) q_sw(t) q_he(t) q_ro(t) q_pi(t) q_d_su(t) q_d_sw(t) q_d_he(t) q_d_ro(t) q_d_pi(t) q_dd_su(t) q_dd_sw(t) q_dd_he(t) q_dd_ro(t) q_dd_pi(t) spar_mass
Rot_mat=[cos(q_pi) sin(q_pi)*sin(q_ro) sin(q_pi)*cos(q_ro);cos(q_pi) cos(q_ro) -sin(q_ro); -sin(q_pi) cos(q_pi)*sin(q_ro) cos(q_pi)*cos(q_ro)];
Inertia_principal_spar=[Ixx_spar 0 0;Iyy_spar 0 0;0 0 0];
Inertia_global_spar=Rot_mat*Inertia_principal_spar*Rot_mat^(-1);
Rot_velocity=[q_d_ro(t);q_d_pi(t);0];
Ec_spar_trans= 0.5*spar_mass*(q_d_su^2 + q_d_sw^2 + q_d_he^2);
Ec_spar_rot= 0.5*Rot_velocity.'*Inertia_global_spar*Rot_velocity;
Ec_spar=Ec_spar_trans+Ec_spar_rot;
Ec_spar_surge=diff(Ec_spar,q_d_su);
Ec_spar_sway=diff(Ec_spar,q_d_sw);
Ec_spar_heave=diff(Ec_spar,q_d_he);
Ec_spar_roll=diff(Ec_spar,q_d_ro);
Ec_spar_pitch=diff(Ec_spar,q_d_pi);
Ec_spar_d_surge=diff(Ec_spar_surge,t);
Ec_spar_d_sway=diff(Ec_spar_sway,t);
Ec_spar_d_heave=diff(Ec_spar_heave,t);
Ec_spar_d_roll=diff(Ec_spar_roll,t);
Ec_spar_d_pitch=diff(Ec_spar_pitch,t);
%%% substitution of the variables
Ec_spar_d_surge=subs(Ec_spar_d_surge,[diff(q_su,t),diff(q_sw,t),diff(q_he,t),diff(q_ro,t),diff(q_pi,t),diff(q_d_su,t),diff(q_d_sw,t),diff(q_d_he,t),diff(q_d_ro,t),diff(q_d_pi,t)],[q_d_su,q_d_sw,q_d_he,q_d_ro,q_d_pi,q_dd_su,q_dd_sw,q_dd_he,q_dd_ro,q_dd_pi]);
Ec_spar_d_sway=subs(Ec_spar_d_sway,[diff(q_su,t),diff(q_sw,t),diff(q_he,t),diff(q_ro,t),diff(q_pi,t),diff(q_d_su,t),diff(q_d_sw,t),diff(q_d_he,t),diff(q_d_ro,t),diff(q_d_pi,t)],[q_d_su,q_d_sw,q_d_he,q_d_ro,q_d_pi,q_dd_su,q_dd_sw,q_dd_he,q_dd_ro,q_dd_pi]);
Ec_spar_d_heave=subs(Ec_spar_d_heave,[diff(q_su,t),diff(q_sw,t),diff(q_he,t),diff(q_ro,t),diff(q_pi,t),diff(q_d_su,t),diff(q_d_sw,t),diff(q_d_he,t),diff(q_d_ro,t),diff(q_d_pi,t)],[q_d_su,q_d_sw,q_d_he,q_d_ro,q_d_pi,q_dd_su,q_dd_sw,q_dd_he,q_dd_ro,q_dd_pi]);
Ec_spar_d_roll=subs(Ec_spar_d_roll,[diff(q_su,t),diff(q_sw,t),diff(q_he,t),diff(q_ro,t),diff(q_pi,t),diff(q_d_su,t),diff(q_d_sw,t),diff(q_d_he,t),diff(q_d_ro,t),diff(q_d_pi,t)],[q_d_su,q_d_sw,q_d_he,q_d_ro,q_d_pi,q_dd_su,q_dd_sw,q_dd_he,q_dd_ro,q_dd_pi]);
Ec_spar_d_pitch=subs(Ec_spar_d_pitch,[diff(q_su,t),diff(q_sw,t),diff(q_he,t),diff(q_ro,t),diff(q_pi,t),diff(q_d_su,t),diff(q_d_sw,t),diff(q_d_he,t),diff(q_d_ro,t),diff(q_d_pi,t)],[q_d_su,q_d_sw,q_d_he,q_d_ro,q_d_pi,q_dd_su,q_dd_sw,q_dd_he,q_dd_ro,q_dd_pi]);
%%% mass matrix
M(1,1)=coeffs(Ec_spar_d_surge,q_dd_su);
M(1,2)=coeffs(Ec_spar_d_surge,q_dd_sw);
M(1,3)=coeffs(Ec_spar_d_surge,q_dd_he);
M(1,4)=coeffs(Ec_spar_d_surge,q_dd_ro);
M(1,5)=coeffs(Ec_spar_d_surge,q_dd_pi);
M(2,1)=coeffs(Ec_spar_d_sway,q_dd_su);
M(2,2)=coeffs(Ec_spar_d_sway,q_dd_sw);
M(2,3)=coeffs(Ec_spar_d_sway,q_dd_he);
M(2,4)=coeffs(Ec_spar_d_sway,q_dd_ro);
M(2,5)=coeffs(Ec_spar_d_sway,q_dd_pi);
M(3,1)=coeffs(Ec_spar_d_heave,q_dd_su);
M(3,2)=coeffs(Ec_spar_d_heave,q_dd_sw);
M(3,3)=coeffs(Ec_spar_d_heave,q_dd_he);
M(3,4)=coeffs(Ec_spar_d_heave,q_dd_ro);
M(3,5)=coeffs(Ec_spar_d_heave,q_dd_pi);
M(4,1)=coeffs(Ec_spar_d_roll,q_dd_su);
M(4,2)=coeffs(Ec_spar_d_roll,q_dd_sw);
M(4,3)=coeffs(Ec_spar_d_roll,q_dd_he);
% c_roll=zeros(1,2);
c_roll
% M(4,4)=c_roll(2);
M(4,5)=coeffs(Ec_spar_d_roll,q_dd_pi);
M(5,1)=coeffs(Ec_spar_d_pitch,q_dd_su);
M(5,2)=coeffs(Ec_spar_d_pitch,q_dd_sw);
M(5,3)=coeffs(Ec_spar_d_pitch,q_dd_he);
M(5,4)=coeffs(Ec_spar_d_pitch,q_dd_ro);
M(5,5)=coeffs(Ec_spar_d_pitch,q_dd_pi);
Could anyone help please ?
Best Regards,
