ESDU 89015 starts by setting out the completely general problem in terms of the equations of motion of the aircraft, the constraints on the state and control variables due to physical or operational limitations, and a performance index which is the quantity to be optimised (for example, time to height). It discusses various simplifications that can then be applied to bring the problem into a solvable form, treating the aircraft as a point mass and ignoring both the rotational motion and airframe flexibility. Although the problem is then reduced to one solvable, it still contains some fourteen equations and some care is needed to justify the use of such complexity; in some cases the performance index will vary quite slowly near the optimum and a trajectory, more easily flown or controlled, a little removed from the true optimum may be acceptable. Finally, the introduction of more simplifications such as assuming that lift equals weight, drag is constant at the level-flight value, or small flight path angle, is considered and the value of the results obtained assessed.