This brief presents several aspects of flight dynamics which are usually omitted or briefly
mentioned in textbooks in a concise self-contained and rigorous manner. The kinematic and
dynamic equations of an aircraft are derived starting from the notion of the derivative of a
vector and then thoroughly analysed interpreting their deep meaning from a mathematical
standpoint and without relying on physical intuition. Moreover some classic and advanced
control design techniques are presented and illustrated with meaningful examples.
Distinguishing features that characterize this brief include a definition of angular velocity
which leaves no room for ambiguities an improvement on traditional definitions based on
infinitesimal variations. Quaternion algebra Euler parameters and their role in capturing the
dynamics of an aircraft are discussed in great detail. After having analyzed the longitudinal-
and lateral-directional modes of an aircraft the linear-quadratic regulator the
linear-quadratic Gaussian regulator a state-feedback H-infinity optimal control scheme and
model reference adaptive control law are applied to aircraft control problems. To complete the
brief an appendix provides a compendium of the mathematical tools needed to comprehend the
material presented in this brief and presents several advanced topics such as the notion of
semistability the Smith-McMillan form of a transfer function and the differentiation of
complex functions: advanced control-theoretic ideas helpful in the analysis presented in the
body of the brief.A Mathematical Perspective on Flight Dynamics and Control will give
researchers and graduate students in aerospace control an alternative mathematically rigorous
means of approaching their subject.
