Browsing by Author "Mathwig, Jarret"
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Item Collision avoidance for aircraft in abort landing(2009) Mathwig, JarretWe study the collision avoidance between two aircraft flying in the same vertical plane: a host aircraft on a glide path and an intruder aircraft on a horizontal trajectory below that of the host aircraft and heading in the opposite direction. Assuming that the intruder aircraft is uncooperative, the host aircraft executes an optimal abort landing maneuver: it applies maximum thrust setting and maximum angle of attack lifting the flight path over the original path, thereby increasing the timewise minimum distance between the two aircraft and, in this way, avoiding the potential collision. In the presence of weak constraints on the aircraft and/or the environment, the angle of attack must be brought to the maximum value and kept there until the maximin point is reached. On the other hand, in the presence of strong constraints on the aircraft and the environment, desaturation of the angle of attack might have to take place before the maximin point is reached. This thesis includes four parts. In the first part, after an introduction and review of the available literature, we reformulate and solve the one-subarc Chebyshev maximin problem as a two-subarc Bolza-Pontryagin problem in which the avoidance and the recovery maneuvers are treated simultaneously. In the second part, we develop a guidance scheme (gamma guidance) capable of approximating the optimal trajectory in real time. In the third part, we present the algorithms employed to solve the one-subarc and two-subarc problems. In the fourth part, we decompose the two-subarc Bolza-Pontryagin problem into two one-subarc problems: the avoidance problem and the recovery problem, to be solved in sequence; remarkably, for problems where the ratio of total maneuver time to avoidance time is sufficiently large (≥5), this simplified procedure predicts accurately the location of the maximin point as well as the maximin distance.Item On properties of the Hohmann transfer(2004) Mathwig, Jarret; Miele, AngeloIn this work, we present a complete study of the Hohmann transfer maneuver between two circular coplanar orbits. After revisiting its known properties, we present a number of supplementary properties which are essential to the qualitative understanding of the maneuver. Specifically, along a Hohmann transfer trajectory, there exists a point where the path inclination is maximum: this point occurs at midradius and is such that the spacecraft velocity equals the local circular velocity. This implies that, in a Hohmann transfer, the spacecraft velocity is equal to the local circular velocity three times: before departure, at midradius, and after arrival. In turn, this allows the subdivision of the Hohmann transfer trajectory into a region where the velocity is subcircular and a region where the velocity is supercircular, with the transition from one region to another occurring at midradius. Also, we present a simple analytical proof of the optimality of the Hohmann transfer and complement it with a numerical study via the sequential gradient-restoration algorithm. Finally, as an application, we present a numerical study of the transfer of a spacecraft from the Earth orbit around the Sun to another planetary orbit around the Sun for both the case of an ascending transfer (orbits of Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto) and the case of a descending transfer (orbits of Mercury and Venus).