I have made a simple model of a vehicle moving along a path $y(x)$.
The goal is to see how the vehicle behaves when a certain tractional force is applied along a path.
I have got the equation as such
$v(t)' = F_t - (g \sin(\beta (x)) +Av^2(t) +Bv(t) + C )$
$\beta(x) = \arctan(dy/dx)$
where $A$, $B$ and $C$ are constants related to friction and air drag. Normally I would develop a state equation system, but I don't think this works due to the non linear nature of the problem.
Any help is appreciated thanks