Solving differential equation system with time dependent condition ?

Hey everyone,

I am trying to solve a system of differential equation using ode function.

My questions about it are the following:

- how to choose the right ode function to use ?

- the tricky part is that I need to set some of the state as a time-dependent function (sin(t) here), there are some explanation about time-dependent coefficient but I found nothing on time-dependent function for state.

Basically I need to impose a trajectory on two states and keeping the other at 0, compute the control u and use it in a cost function to be minimized, giving me the best angle to use for the propeller (alpha & beta).

For information here is my system: p(t) vector of position (x,y,z) (p_dot, p_dot_dot derivative), R(t) vector of angle (phi,theta,psi) (w speed angle vector, w_dot acceleration angle vector). It's about a drone with six propellers (u is control vector of the speed of rotation of the propeller)

w_dot = -inv(J)*cross(w,J*w)+inv(J)*F2*u

p_dot_dot= [0;0;-g] + (1/M)*wRb*F1*u

F1,F2,J are constant matrix, wRb a rotation matrix changing with orientation state R(t)

Thanks in advance, don't hesitate to ask for further detail if need

(PS: I put my different file in joint-file, as a french guy the name can be confusing so here are the translation:

optimisation = optimization (main file)

contrainte = constraint (non-linear constraint file)

wrench = the file enabling me to compute the control u from the solution of equation

dynamique = dynamic (file describing the system of equation)

solveur = solver (the function calling the ode function)