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The calculus of variations and energy-state approximation are used to determine the optimum maneuvers in three-dimensional minimum-time aircraft flight paths to a specified final point or line. Constraints on thrust, Mach number, angle of attack, dynamic pressure, and load factor are included. It is shown that when the initial range is sufficiently large that the maximum velocity constraint is encountered en route, the calculation of minimum-time maneuvers can be greatly simplified by a separation of arcs into two two-parameter problems. Suboptimal paths along which the bank angle is restricted to three discrete values (negative maximum angle, 0, positive maximum angle) compare favorably with the optimum, continuous bank angle solutions for transonic speeds and below.

V/STOL aircraft automatic flight control, guidance and navigation by onboard computer, discussing mathematical model and simulation results

Subsonic glide landing approach guidance for unpowered lifting vehicles, using perturbation feedback and approximation of heading and position coordinates

(1965). Solution of the Initial Value Problem for the Riccati Equation. The American Mathematical Monthly: Vol. 72, No. 3, pp. 270-275.

A theoretical model for the visual integrative process is advanced that is based upon microelectrode studies of the animal visual cortex by Hubel and Wiesel, Jung, and others. In this theoretical model the cortical columns of directionsensing elements found by Hubel and Weisel are interpreted as sets of isoclines making up the visual field. The form of a visual image corresponds to a family of contours ('orbits' or 'paths', in the terminology of differential equations) that pass through those isoclines stimulated by the corresponding retinal regions. A contour of an image is thus approximated in the visual cortex as an isoclinic polygonal arc. Hubel and Wiesel's microelectrode studies are thus strongly suggestive of a differential equation interpretation of the visual integrative process. The invariance of the visual integrative process under rigid motions (translation and rotation) and perspective that is required by the psychological phenomenon of Gestalt enables us to specify the particular form of the differential equations involved.

Energy state approximation for supersonic aircraft performance optimization with extension to maximum range problems, noting comparison with complex dynamic models

It is postulated that at least some types of whistler signals, e.g., ‘long trains,’ are generated by synchronous interaction between an energetic upward discharge from the top of a thundercloud and the extraordinary component of a sferic that lags the discharge by a time of the order of a second. The nature of the over-all generation mechanism is outlined, and the evidence for each phase is reviewed. An elementary theory of the synchronous interaction is stated.