Linear lateral dynamics

The second order (two degree of freedom) Dutch-Roll approximation is an approximation to the abovefourth 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 : 

The second order roll equations above amount simply to the ?rst order equation :