I'm trying to solve a 1 DOF second order differential equation for theta(t),
theta_dd(t) = -(m1*g*sin(theta)+T2*sin(theta+beta)+m1*x_dd(t))/(m1*l1)
where beta and T2 are both function of theta, and x_dd(t) is a forcing function.
beta = @(theta) asin((l1/l2)*sin(theta));
T2 = @(theta) (m2*ydd+c*yd+k1*y+m2*g)./cos(beta(theta));
T2 is dependent on ydd(t), yd(t), y(t), and beta, again all of which are dependent of theta(t). My question is are how I can use matlab to define the first and second derivative of y(t).
y = @(theta) l1*(1-cos(theta))+l2*(1-cos(beta(theta)));
yd = @(theta) ...;
ydd = @(theta) ...;
I'm going to run this on simulink but i need to provide a function for T2.
Some have recommended using the symbolic toolbox but I'm not sure where to start.