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针对常值推力下航天器面内轨道转移燃耗最省的轨道优化问题,利用极大值原理导出了最优轨迹下推力方向角应满足的控制方程,结合动力学方程建立了一种求解航天器面内最优转移轨道的改进间接法,及其在推力方向角调节能力受限条件下的应用方法。由于避免了协态变量微分方程组的求解,改进间接法相对于传统间接法降低了初值猜测的难度和计算量;与采用Gauss伪谱法求解相比,所建立的改进间接法求解结果精度更高,数值光滑性更好。仿真算例表明:推力方向角调节能力受限会改善推力方向角变化规律,降低推力方向角变化范围;就燃耗而言,推力越大燃耗越多,优化轨道节省燃耗更加显著。
In order to solve the orbit optimization problem of the most province-wide orbital fuel economy under constant thrust, the governing equation of the thrust direction angle under the optimal trajectory is derived by using the maximum principle. A new aerodynamic equation An Improved Indirect Method for Optimal Transfer Orbit in a Plane and Its Application in a Condition of Limited Thrust Angle Adjustment Capability. Compared with the traditional indirect method, the improved indirect method reduces the difficulty and computational complexity of the initial guess because of avoiding the solution of the covariate differential equations. Compared with the Gauss pseudo-spectral method, the accuracy of the improved indirect method High, the numerical smoothness is better. The simulation results show that the limited ability to adjust the thrust direction angle will improve the change rule of the thrust direction angle and reduce the variation range of the thrust direction angle. In the case of fuel consumption, the larger the thrust force, the more the fuel consumption, and the more optimized orbit fuel saving is more significant.