Abstract
Minimum time trajectories for highly maneuverable aircraft with high thrust to welght ratios tend to be in the vertical plane. The singularity in path inclination of the equations of motion defined with Euler angles can be avoided by using quaternions instead. In this new system of equations the velocity bank angle is replaced by a new control variable which is proportional to the bank angle turn rate and appears linearly in the new differential equations. Therefore the optimal solution may consist of singular subarcs.For the numerical solution of this problem a nonlinear programming technique is used to find the optimal sequence of subarcs and a multiple shooting method is taken to compute the exact solution. Merits and disadvantages of these two approaches for solving singular optimal control problems are discussed based on numerical results for several optimal aircraft trajectories.
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