Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
复制标题
DOI：
10.1016/j.anihpc.2006.03.013
复制
发表时间：
2007-05
影响因子：
1.9
通讯作者：
B. Bonnard;Jean-Baptiste Caillau
中科院分区：
文献类型：
--
作者：
B. Bonnard;Jean-Baptiste Caillau
本文以Epenoy等人的初步结果为基础，研究了低推力下卫星在开普勒型轨道之间的最优转移问题。(1997)，其中能量最小化问题的最优轨迹使用平均技术来近似。显式计算了平均哈密顿系统。它涉及到一个黎曼问题，该问题的距离是值函数的近似值。对极值曲线进行了分析，证明了系统在共面情况下是可积的。还检查了与朝向圆形轨道的共面转移相关联的度规是平坦的。小黎曼球面的光滑性确保了计算极值的全局最优性。
This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion and is based on preliminary results of Epenoy et al. (1997) where the optimal trajectories of the energy minimization problem are approximated using averaging techniques. The averaged Hamiltonian system is explicitly computed. It is related to a Riemannian problem whose distance is an approximation of the value function. The extremal curves are analyzed, proving that the system remains integrable in the coplanar case. It is also checked that the metric associated with coplanar transfers towards a circular orbit is flat. Smoothness of small Riemannian spheres ensures global optimality of the computed extremals.