...
In the earth reference frame newtons newton's second law holds such that:
...
Linearization
Model linearization consists is the process of simplifying the equations of motion using a first order taylor expansion at some trim state. In this simulation, the nonlinearity of the state equations is not an issue as they can be reliably solved using numerical integration. The nonlinearity of the forces, however, poses a significant modelling challenge however as “They are not part of the state of the aircraft. Instead they also depend on the state of the aircraft. And they don’t only depend on the current state, but on the entire history of states! (For example, a change in angle of attack could create disturbances at the wing. These disturbances will later result in forces acting on the tail of the aircraft.)” [2]
In practice many of these nonlinear force relationships can be neglected, however, several significant non-linear relations remain. Mathematically this is shown by:
...