using coeff(f,[])

Hello

so i am using this function.

syms theta1(t) psi1(t) xh(t) theta2(t) psi2(t) yh(t) zh(t) m J l 
%position of each center of mass of each cylinder 
x1 = xh+2*l+l*cos(theta1)*cos(psi1);
y1 = yh+l*sin(psi1);
z1 = zh+l*sin(theta1);
x2 = xh+2*l+2*l*cos(theta1)*cos(psi1)+l*cos(theta2)*cos(psi2);
y2 = yh+2*l*sin(psi1)+l*sin(psi2);
z2 = zh+2*l*sin(theta1)+l*sin(theta2);
%derivatives of each position
x1_dot = diff(x1,t);
x2_dot = diff(x2,t);
y1_dot = diff(y1,t);
y2_dot = diff(y2,t);
z1_dot = diff(z1,t);
z2_dot = diff(z2,t);
% Lagrange equation, calculate dT/dq of each state space :
T=1/2*m*(x1_dot^2)+0.5*m*diff(xh,t)^2+(1/2)*m*(y1_dot^2)+0.5*m*diff(yh,t)^2+(1/2)*m*(z1_dot^2)+0.5*m*diff(zh,t)^2+(1/2)*J*diff(theta1,t)+(1/2)*J*diff(psi1,t);
% calculating each dT-dq
dT_xhdot=diff(T,diff(xh,t));
DdT_xhdot_dT=diff(dT_xhdot,t)
[ coeff,state]=coeffs(DdT_xhdot_dT,[diff(xh,t,t) diff(theta1(t),t,t) diff(psi1(t), t,t) diff(theta1(t), t)*diff(psi1(t), t)])
%diff(psi1(t), t,t) diff(theta1(t),t,t) (diff(theta1(t),t))^2 (diff(psi1(t),t))^2

where i get this results :

m*diff(xh(t), t, t) - (m*(2*l*cos(psi1(t))*cos(theta1(t))*diff(psi1(t), t)^2 - 2*diff(xh(t), t, t) + 2*l*cos(psi1(t))*cos(theta1(t))*diff(theta1(t), t)^2 + 2*l*cos(theta1(t))*sin(psi1(t))*diff(psi1(t), t, t) + 2*l*cos(psi1(t))*sin(theta1(t))*diff(theta1(t), t, t) - 4*l*sin(psi1(t))*sin(theta1(t))*diff(psi1(t), t)*diff(theta1(t), t)))/2

Error using symengine

Invalid indeterminate.

Error in sym/mupadmexnout (line 1092)

out = mupadmex(fcn,args{:});

Error in sym/coeffs (line 63)

[cSym,tSym] = mupadmexnout('symobj::coeffsterms', p, args{:});

Error in snakelagrange (line 25)

[ coeff,state]=coeffs(DdT_xhdot_dT,[diff(xh,t,t) diff(theta1(t),t,t) diff(psi1(t), t,t) diff(theta1(t), t,

t)*diff(xh(t), t, t)],'All')

the code give me coeff for diff(xh,t,t) diff(theta1(t),t,t) diff(psi1(t), t,t) but once i am using diff(theta1(t),t)*diff(psi1(t), t) i get this error. i believe it has do with my syms definition. Does anyone know how to solve this ?

i also need the coeff expressed in diff(theta1(t),t)^2 which is not working either

Answer 1

[Shishir Reddy]

Hi Elio

The issue you're encountering is related to the coeffs function in MATLAB, which is designed to extract coefficients of polynomials. However, if it is used with non-polynomial expressions (like products of derivatives), it can lead to errors.

Kindly refer to the following code snippets to understand where the changes have to be made in the provided code to address this issue.

1. Define Temporary Variables

syms dtheta1 dpsi1 dxh

2. Replace the derivative terms in your expression with these temporary variables

DdT_xhdot_dT_sub = subs(DdT_xhdot_dT, ...
    [diff(xh, t, t), diff(theta1(t), t, t), diff(psi1(t), t, t), diff(theta1(t), t), diff(psi1(t), t)], ...
    [dxh, dtheta1, dpsi1, dtheta1, dpsi1]);

3. Simplify the expression after substitution

DdT_xhdot_dT_simplified = simplify(DdT_xhdot_dT_sub);

4. Extract the coefficients by substituting back to isolate each term

coeff_xh_tt = subs(DdT_xhdot_dT_simplified, [dtheta1, dpsi1, dxh], [0, 0, 1]);
coeff_theta1_tt = subs(DdT_xhdot_dT_simplified, [dtheta1, dpsi1, dxh], [1, 0, 0]);
coeff_psi1_tt = subs(DdT_xhdot_dT_simplified, [dtheta1, dpsi1, dxh], [0, 1, 0]);
coeff_theta1_dpsi1 = subs(DdT_xhdot_dT_simplified, [dtheta1, dpsi1, dxh], [1, 1, 0]);

5. Finally, display the coefficients as needed

coeff_xh_tt
coeff_theta1_tt
coeff_psi1_tt
coeff_theta1_dpsi1

For more information regarding the subs function, kindly refer the following documentation - https://www.mathworks.com/help/symbolic/sym.subs.html

I hope this resolves the issue.