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Stability in Aerspace Systems

Is stability a measurable quantity — like mass or an
identifiable quantity - like temperature? There are many
definitions of stability, sometimes contradictory: in fact,
it is a subjective quantity which should be defined in the
context of the theme considered. The reference system in
which the system evolves should be defined: stability
may exist in a given reference system, but no longer
exists in other reference systems. Stability seems to be a
dominant factor for aircraft or missile control — or any
type of vehicle. However, stability and manoeuvrability
are two opposing factors which intervene in aircraft
control: for civilian aircraft stability is the deminant
factor; for military aircraft or missiles manoeuvrability is
the dominant factor. The above are some of the reasons
which led to the organization of a Workshop on
"Stability" for the AGARD community.

Basically, stability is related to irreversibility which
means energy dissipation for linear systems, but linear
systems are very rare though they also often represent a
suitable approximation of non linear systems. Stability is
also a matter of accuracy. Let’s take the earth’s rotation:
is it stable or unstable? This question has no meaning
until the range of accuracy we are looking for, and in
fact, the whole context is specified. Due to the accuracy
of existing atomic clocks, it is demonstrated that daily
variations are of the order of lms yearly or pluri—annual
variations of the order of tens of ms, occur in a pseudo
periodic manner. However, the angular velocity is
necessarily decreasing on a long-range basis: this is
mainly due to the water/earth friction of tides. In the pre-
Cambrian period (400 M years) the day was 15 hours!
What has been said about the angular velocity of the
earth could also be said about the direction of the earth’s
momentum. At the pole the trace of the rotational vector
moves continuously in a circle of about 2m in diameter.
However, for all human activities the earth’s rotation is
considered (except by some astronomers) as stable.

Poincare in the 18708 studied stability for non-
autonomous and autonomous problems. Ljapounov in the
19005 introduced a way of proving whether or not
stability was sufficient, but not the necessary conditions.
Thereafter the behaviour of a system in the vicinity of an
"equilibrium point" was studied in detail (Poincare) and
equilibrium points or "singularities" were classified as
nodes-summits-focus-saddle.