过载限制下气动力辅助变轨的最优解与平衡滑行解

Optimal Aeroassisted Orbital Plane Change with Deceleration Constraint and Equilibrium Glide Solution

基于庞特里亚金最大值原理 ,获得了最优飞行轨迹中升力系数和滚转角的表达式以及平衡滑行解。平衡滑行中航迹角很小并且保持近似恒定。在数值优化计算中 ,初始值的估计是非常困难的。由于平衡滑行附近的近似解与精确最优解是很接近的 ,这意味着可以以平衡滑行解作为优化分析中的初始值 ,从而克服了初始值估计的难题。

This paper gives a general assessment of the optimal aeroassisted orbital plane change with deceleration constraint. By nature, the computation of optimal guess of unknown arguments will lead to some difficulties in numerical calculation. Using Pontryagin maximum principle, the optimal expression of lift coefficient and bank angle during flight are derived, and the equilibrium glide solutions, in which the flight path angle is small and stays nearly constant, are also derived. It is interesting that the optimal solution under the equilibrium glide condition is very close to the exact optimal solution. Hence it means that the equilibrium glide solution is a very good suboptimal solution and it can be selected as a intial guess of unknown arguments to alleviate the difficulties in the computation.