Treatment of Stability and Control
As with a fixed-wing aircraft, both static stability and dynamic stability contribute to the flying qualities of a helicopter. Static stability refers to the initial tendency of the aircraft to return to its trimmed condition following a displacement. Dynamic stability considers the subsequent motion in time, which may consist of a dead-beat return, an oscillatory return, a no-change motion, an oscillatory divergence or a non-return divergence; the first two signify positive stability, the third neutral stability and the last two negative stability (instability). A statically unstable motion is also dynamically unstable but a statically stable motion may be either stable or unstable dynamically.
The subject of stability and control in totality is a formidable one. The part played by the rotor is highly complicated, because strictly each blade possesses its own degrees of freedom and makes an individual contribution to any disturbed motion. Fortunately, however, analysis can almost always be made satisfactorily by considering the behaviour of the rotor as a whole. Even so it is useful to make additional simplifying assumptions: those which pave the way for a classical analysis, similar to that made for fixed-wing aircraft, come essentially from the work of Hohenemser  and Sissingh  and are the following:
• in disturbed flight the accelerations are small enough not to affect the rotor response, in other words the rotor reacts in effect instantaneously to speed and angular rate changes;
• rotor speed remains constant, governed by the engine;
• longitudinal and lateral motions are uncoupled so can be treated independently. (Strictly speaking, longitudinal and lateral motions are in fact coupled. However, they can be considered uncoupled for a first analysis. Examples of situations where coupling is significant are:
– roll manoeuvres;
– lateral disc tilt induced by forward flight;
– tail rotor thrust.
Cross-coupling is present in situations such as these and has significant effects on the handling qualities.)
Given these important simplifications, the mathematics of helicopter stability and control is nevertheless heavy (Bramwell’s Chapter 7), edifying academically but hardly so otherwise, and in practice strongly dependent upon the computer for results. In this chapter we shall be content with descriptive accounts, which bring out the physical characteristics of the motions involved.
No absolute measure of stability, static or dynamic, can be stipulated for helicopters in general, because flying qualities depend on the particular blend of natural stability, control and autostabilization. Also, stability must be assessed in relation to the type of mission to be performed.