AI 中文总结
本文基于诺特定理，修改拉格朗日量后构建基灵方程，推导中心引力场中航天器最优连续推力轨道的三个新守恒量，经数值模拟和数学证明验证其守恒性。
AI 中文摘要
本文针对中心引力场中航天器在最优连续推力轨道运动中的三个新守恒量，开展了数学推导。该推导过程基于诺特定理，该定理将动力系统的点对称性与系统对应的守恒律关联起来。本文采用的方法中，为考虑非保守控制力，对系统的拉格朗日量进行了修改，利用该广义拉格朗日量写出待最小化的作用量泛函，随后构建基灵方程以求解该系统的动力对称性。本文明确了求解基灵方程的流程，将诺特定理应用于基灵方程的解，得到系统的守恒量，给出了二维和三维轨道在多种不同坐标系下的守恒量，并通过数值模拟和数学证明验证了所计算的守恒量具有守恒性。
英文摘要
This paper presents a mathematical derivation for three new conserved quantities in the motion of spacecraft on optimal continuous-thrust trajectories in a central gravitational field. The process presented in this paper is rooted in Noether's theorem that connects the point symmetries of a dynamic system with the associated conservation laws of the system. In the approach presented in this paper, the system's Lagrangian is modified to account for the non-conservative control force. Using this generalized Lagrangian, the action functional to be minimized is written. Then, Killing equations are formulated to find the dynamic symmetries for this system. In this paper a process is laid out for how to solve the Killing equations; Noether's theorem is applied to this solution of the Killing equations to write the conserved quantities of the system. Conserved quantities are presented for both the two-dimensional and the three-dimensional trajectories in several different coordinate frames. Numerical simulations and mathematical proofs are used to demonstrate that the computed quantities are conserved.
Comments20 pages, 6 figures
