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首页> 外文期刊>Mathematical Problems in Engineering: Theory, Methods and Applications >Optimization of Low-Thrust Limited-Power Trajectories in a Noncentral Gravity Field—Transfers between Orbits with Small Eccentricities
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Optimization of Low-Thrust Limited-Power Trajectories in a Noncentral Gravity Field—Transfers between Orbits with Small Eccentricities

机译：非中心重力场中低推力极限动力轨迹的优化-小偏心距轨道之间的传递

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Numerical and first-order analytical results are presented for optimal low-thrust limited-powertrajectories in a gravity field that includes the second zonal harmonicJ2in the gravitational potential. Only transfers between orbits with small eccentricities are considered. The optimization problem is formulated as a Mayer problem of optimal control with Cartesian elements—position and velocityvectors—as state variables. After applying the Pontryagin Maximum Principle, successive canonicaltransformations are performed and a suitable set of orbital elements is introduced. Hori method—aperturbation technique based on Lie series—is applied in solving the canonical system of differentialequations that governs the optimal trajectories. First-order analytical solutions are presented fortransfers between close orbits, and a numerical solution is obtained for transfers between arbitraryorbits by solving the two-point boundary value problem described by averaged maximum Hamiltonian,expressed in nonsingular elements, through a shooting method. A comparison between analytical andnumerical results is presented for some maneuvers.
机译：给出了在重力场中包括第二个纬向谐波J2的重力场中最佳低推力有限功率轨迹的数值和一阶分析结果。仅考虑偏心率小的轨道之间的转移。最优化问题用笛卡尔元素（位置和速度矢量）作为状态变量来表述为最优控制的Mayer问题。应用庞特里亚金最大原理后，将进行连续的规范变换，并引入一组合适的轨道元素。 Hori方法（基于李序列的摄动技术）被用于求解控制最优轨迹的典型微分方程系统。给出了近轨道之间传递的一阶解析解，并通过射击方法求解了用非奇异元素表示的平均最大哈密顿量所描述的两点边值问题，得到了任意轨道之间传递的数值解。提出了一些分析结果和数值结果之间的比较。

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