A dogfight between two aircraft each represented by a point mass in a horizontal plane of constant speed with bounded turning capability is examined. A number of complexities associated with this problem are avoided by the way the capture zones for each of the players are defined. However, by so doing, the possible outcomes of mutual destruction and draw are not distinguishable from a win by each of the players. Both the methods of Qualitative Game Theory and Control Theory are used in the analysis of a particular example. Two regions of state space of interest to the first aircraft are delineated. These regions have the property that if the second aircraft is located in the first region, the first aircraft can win the dogfight; however, if the second aircraft is located in the second region, then the first aircraft may lose the dogfight.
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