The second order (two degree of freedom) Dutch-Roll approximation is an approximation to the above fourth order system for the Dutch Roll dynamics. A justification for this is to consider the roll dynamics decoupled from the sideslip and yaw associated with the Dutch Roll motion by assuming that the coupling terms are negligble. In particular it is assumed that there is 1 :
• straight and level flight so that γ_{0} = 0• a negligible effect due to gravity so that g (φU_{0})= 0• a negligible rolling acceleration from yaw rate so that L′_{r} = 0• a negligible yawing acceleration from roll rate so that N′_{p} = 0• a negligible rolling acceleration from sideslip so that L′_{β} = 0With these assumptions the fourth order state space equation above becomes