Advanced Flight Dynamics

Here is a crash introduction formal flight dynamics with some tricky AWE issues and their proposed theoretic resolution:
Three Galilean frames-of-reference are common in flight modeling; the Earth Frame, the aircraft Body Frame, and the Wind Frame. A combinatoric explosion occurs in reconciling multiple frames, so its very hard to calculate flight Control Theory problems in real-time, especially with added complications like control actuation dynamics, wind frame turbulence, body aeroelasticity, and wake-interactions, not to mention a Tether Frame. All these motions have complex force moments to account for, constantly cycling between potential and kinetic energy as interacting harmonic oscillators.
The body frame has three Angles of Rotation, Yaw, Pitch, and Roll, that are treated in fixed order when calculating Euler Angles between frames. Furthermore, there are three Motions of Translation, Surge, Heave, and Sway. These are the six basic Degrees-of-Freedom (DOF) of a body in 3D space (with time as a forth dimension and even sonic-relativity according to tether tension cycling to account for). All aircraft in flight experience continuous oscillation along these six DOF, but simplified flight modeling neglects translation modes, sweeping messy deterministic dynamics under a rug of imaginary-number exponents.
The wind frame is incredibly more complex than the simplest frozen field assumption, and all  turbulence models used in AWE so far are crude approximations. The one fairly tractable frame is the earth frame, where a fixed-position assumption is adequate (but even the earth frame dances minutely with every kite).
A mathematical case for dense cross-linked AWES arrays with spread multiple-anchor fields is tenable based on the notion that the body frame can be eliminated in calculations by close physical integration of the body with the earth frame. This “constraint network” approach makes associated constraint-resolution problems far more tractable. Including wind frame turbulence becomes more tractable, since an aggregated larger AWES unit scale is immune to small-scale turbulence that can thus be ignored. Moreover, a single Control Thread then suffices to control the whole kitefarm, rather than disparate units each jostling with their own dedicated auto-pilot.
“Passive control” by integrated static and dynamic stability principles is a radical Open-AWE simplification of AWES control theory that has been a decade in the making.

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