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In the optimal guidance laws of proportional navigation, the problems are mostly formulated to obtain the optimal magnitude of applied commanded acceleration under pure or true proportional navigation. In this paper, the optimal direction of applied commanded acceleration is derived under conventional proportional navigation with a maneuvering or nonmaneuvering target, in which the line-of-sight deflection angle and the energy expenditure until intercept are minimized. Some related important characteristics, such as capture criterion and energy expenditure, are investigated and discussed in detail. Also, a typical example of target maneuver is introduced to illustrate the effect of target maneuver easily. It shows that the target maneuver will decrease the capture area and increase the energy cost for effective intercept of target.
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