Physical systems where the control inputs appear nonlinearly are rather uncommon. They are, however, indispensable in the high-fidelity modeling of aircraft dynamics, where the control surfaces such as the elevator, aileron, and rudder affect the aerodynamic forces and moments of the aircraft in a nonlinear manner.
The six-degree-of-freedom model in body coordinates, where are the inertia terms.
The longitudinal dynamics are the dynamics for states , , , and :
The lateral dynamics are the dynamics for the states , , , and :