Aim:
I want to solve the 6DOF equations to model the flight dynamics of an aircraft (for a flight simulator) In order to do this, I need to solve multiple differential equations using the Runge-Kutta 4 algorithm.
After a bit of research, I can use the RK4 algorithm to solve simple 2 variable ODE's, but I have no idea how to apply it to multi-variable ODE's.
I only have an engineering background so I apologize if I have made a meal out of the terminology.
The equations are a bit hefty so I will only type one of them out... See pg 10/32 for the full set of equations Link to full set of equations.
Equations of Flight
Time Derivative of Angle of Attack $$ \dot\alpha = \frac{\bar q S}{mV}C_Ncos(\alpha) + q-\tan(\beta)(p \cos(\alpha)+r \sin(\alpha) + \frac{g}{V}(\cos(\phi)\cos(\theta)\cos(\alpha)+\sin(\theta)\sin(\alpha)) $$
In these equations most of the variables are functions of time (like $ \dot \alpha, \bar q, V, p,q,r) $
As a result, I am not sure how to proceed. I would be very grateful if someone could offer some help. Alternatively, if anyone has any experience of flight sims I would be delighted to learn how the number-crunching works.
Regards,
Henry