By Jean-Luc Boiffier
The 1st of 3 volumes at the idea and perform of flight dynamics. quantity 1 describes the equations for the final case of a round rotating earth, that's then evaluated via exam of the flat, fastened earth, and provides equations designed to resolve sensible difficulties encountered through aeronautical engineers.
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Extra info for The dynamics of flight: the equations
It involves “isolating” certain equations out of the total of twelve, without affecting the quality of the results with this reduced system. 4, p. 1, p. 135), that is t o say geographical position x , y and azimuth $ with respect t o the other equations. This decoupling is absolutely rigorous in the case of the flat and fixed Earth hypotheses. Without them, only the longitude can be decoupled rigorously. 2, p. 137), which then allow the use of only the five decoupled longitudinal equations. This decoupling is rigorous with certain hypotheses which have often been proved.
It should be noted that linearization around a steady state flight with wind modifies the state matrix with respect t o steady state flight without wind. This means that modes and, therefore, flying qualities can depend on the wind. With linearization around straight horizontal steady state flight without wind, it appears that lateral equations are really decoupled. 2, p. 283). Finally, the last simplification case, Equilibrium (Section 7, p. 179), is a specific case of general flight dynamics equations.
A difference exists between these two latitudes but in a matter of importance that remains inferior to the detailed accuracy searched for in practical studies of Flight Dynamics. The deviation is of the order of 10-4 rad. Finally, the latitude previously defined Lto is called geographical latitude. It is the geocentric latitude when the Earth is assumed to be spherical. The vector g of acceleration due to gravity defining the vertical in 0 , has to all intents and purposes the definite direction by the geodesic latitude.