The idea of stability derivatives is to approximate the general functional relationship between any force ormoment variable and the dynamic or control variables as a Taylor series expansion of the perturbation (i.e.small changes) about a trimmed flight condition. In non mathematical terms this simply means that weassume that we can approximate the functional relationship of the perturbation as a linear combinationof of the dynamic variables and control variables with the coeficients of these termed aerodynamicderivatives. Thus for example the perturbation z of the vertical force Z is expressed in terms of theperturbations of dynamic variables u, uw, w etc. and control variable terms such as due to the elevator
where the partial derivative coeficients are assumed constant at each particular flight condition.