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Singular subarcs arise in quite a few problems of flight dynamics. The present study is devoted to the specific problem of ascent and acceleration of a vehicle in atmospheric flight in which a variable-thrust arc forms a part of the optimal trajectory. A two-parameter family of singular arcs was generated for time-range-fuel problems of an ascending rocket, using the modelling of Zlatskiy and Kiforenko. The short-term optimality of the singular subarcs has been checked in terms of certain necessary conditions: the classical Clebsch condition, the Kelley condition or the Generalized Legendre-Clebsch condition and the Goh condition. All these are found to be satisfied computationally for all the candidates. The calculations were repeated for simplified thrust-along-the-path modelling and similar results on optimality obtained.

Optimal intercept trajectories for a boost-sustain-coast medium-range air-to-air missile are synthesized using optimal control theory. Optimality in time/range/energy at intercept of a target is the main objective. Attainable sets and their boundaries are obtained and used to generate optimal intercept points in a three-dimensional scenario. A three-phase closed-loop guidance scheme is used to generate an efficient guidance law against a maneuvering target. In the present study, target maneuvers are restricted to the horizontal plane. An initial boost-phase with near-optimal guidance in the presence of active control constraints and thrust switches is simulated. Target maneuvers are neglected during this phase. A new method of gain evaluation is detailed. A midcourse guidance scheme with neighboring guidance, transversal comparisons, and chasing center-of-attainability of target to augment performance is studied. Modifications in terminal guidance using proportional navigation, such as chasing the center-of-attainability of target, altitude shaping, and drag-resolution schemes are used to attempt better performance at intercept. A composite guidance strategy using a combination of neighboring guidance and proportional navigation for the midcourse guidance is introduced. The excellent performance of this guidance strategy and the improvement in storage requirements for on-board use make it a very special scheme.