How would you I write a matlab function for theta that represents the 2nd order differential of the torque equation?

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The 2nd order differential equation for the torque is given by:
Matrices for D, C,G and F:
My code:
function torque = fcn(dq,q,T)
% length of the 2 robotic arms
l1 = 1;
% mass of the 2 robotic arms
m1= 5;
% moment of inertia of the 2 robotic arms
I1= (m1*l1^2)/3;
I2 = (m2*l2^2)/3;
p1= m1*r1^2+m2*l1^2+I1;
p2= m2*r2^2+ I2;
p3= m2*l1*r2;
p4= m1*r1+m2*l1;
p5= m2*r2;
% Gravitational strength constant
g = 9.81
D= [p1+p2+2p3*cos(q2) p2+p3*cos(q2); p2+p3*cos(q2) p2];
C= [-p3*dq2sin(q2) -p3(dq1+dq2)sin(q2); p3*dq1*sin(q2) 0];
G= [p4*g*
I am terribly stuck on writing the code for matrix D, C, and G. I don't understand how to express theta in differential terms. Can someone help me?

Accepted Answer

Alan Stevens
Alan Stevens on 27 Jan 2022
Edited: Alan Stevens on 27 Jan 2022
Does this help?
% Theta seems to have two components, so:
D(theta) = [p1+p2+2*p3*cos(theta(2)) p2+p3*cos(theta(2));
p2+p3*cos(theta(2)) p2];
% For thetadot use omega, so, for example:
C(theta, omega) = [-p3*omega(2)*sin(theta(2)) -p3*(omega(1)+omega(2))*sin(theta(2));
p3*omega(1)*sin(theta(2)) 0];
% Replace the 2nd order ODEs by two 1st order ODEs,e.g.something like:
% dthetadt = omega
% domegadt = D(theta)\(tau-F(omega)-G(theta)-C(theta,omega)*omega);

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