基于李雅普诺夫的小推力最优轨道转移：一种直角坐标方法
Lyapunov-based Low-thrust Optimal Orbit Transfer: An approach in Cartesian coordinates
摘要：
本文提出了一种利用直角坐标系统求解两个椭圆轨道之间的小推力最优燃料和最优时间转移问题的简单方法。在这种情况下，轨道由其特定的角动量和具有自由注入点的拉普拉斯矢量来描述。轨迹优化与伪谱方法和非线性规划支持的初始猜测产生的Chang-Chichka-Marsden基于李亚普诺夫转移控制器。这种方法成功地解决了几个小推力优化问题。数值结果表明，基于李雅普诺夫的初始猜测克服了直角坐标系统中变量强烈振荡给优化带来的困难。结果表明，利用直角坐标通过多项式逼近得到最优转移解比利用轨道根数得到最优转移解容易，因为轨道根数通常会产生强非线性运动方程。本文不考虑地球扁率和阴影效应。
英文摘要：
This paper presents a simple approach to low-thrust optimal-fuel and optimal-time transfer problems between two elliptic orbits using the Cartesian coordinates system. In this case, an orbit is described by its specific angular momentum and Laplace vectors with a free injection point. Trajectory optimization with the pseudospectral method and nonlinear programming are supported by the initial guess generated from the Chang-Chichka-Marsden Lyapunov-based transfer controller. This approach successfully solves several low-thrust optimal problems. Numerical results show that the Lyapunov-based initial guess overcomes the difficulty in optimization caused by the strong oscillation of variables in the Cartesian coordinates system. Furthermore, a comparison of the results shows that obtaining the optimal transfer solution through the polynomial approximation by utilizing Cartesian coordinates is easier than using orbital elements, which normally produce strongly nonlinear equations of motion. In this paper, the Earth's oblateness and shadow effect are not taken into account.
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