The problem of determining cruise-dash trajectories is examined for the case of time-fuel optimization using a linear combination of time and fuel as the performance index. The trajectories consist of a transient arc followed by a steady-state arc. For cases where the steady-state arc is flown with full throttle the associated skeletal transient trajectories are also flow with full throttle,and the cruise-dash points are approached monotonically in an asymptotic fashion. When the steady-state arc is flown at an intermediate throttle setting,the transient trajectories follow a singular control law and exhibit a complex structure that is different from the full-throttle transients. Addressing the question of optimality of the steady-state arc,it was found that although steady-state cruise fails a Jacobi-type condition,steady-state cruise-dash can satisfy this condition if the emphasis on time is sufficiently large. The outcome of the Jacobi test appears to be connected with the eigenstructure of the linearized state-adjoint system.
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