Computation and Applications of an Orbital Dynamics Symplectic State Transition Matrix
Computation and Applications of an Orbital Dynamics Symplectic State Transition Matrix
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DOI：
10.2514/1.42358
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发表时间：
2009-07
影响因子：
2.6
通讯作者：
Y. Tsuda;D. Scheeres
中科院分区：
文献类型：
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作者：
Y. Tsuda;D. Scheeres
本文给出了一种求任意哈密顿动力系统辛状态转移矩阵的数值方法。它提供了线性化哈密顿系统的精确解空间映射，保留了所有哈密顿系统本质上应该具有的辛结构。辛状态转移矩阵可以应用于精确且计算效率高的动态滤波器、编队飞行航天器运动的长期传播、n体动力学的特征结构/流形分析等，当精确的结构保持特性至关重要时。给出了辛状态转移矩阵的推导和关键特征，并将其应用于二体动力学、圆形受限三体问题和基于实际星历的摄动地球轨道。这些数值算例表明，与传统的具有欧拉积分或龙格-库塔积分的线性状态转移矩阵相比，该数值辛状态转移矩阵在保持状态转移矩阵的结构性质方面有了改进。
This paper presents a numerical method for deriving a symplectic state transition matrix for an arbitrary Hamiltonian dynamical system. It provides the exact solution-space mapping of the linearized Hamiltonian systems, preserving the symplectic structure that all Hamiltonian systems should possess by nature. The symplectic state transition matrix can be applied to accurate, yet computationally efficient, dynamic filters, long-term propagations of the motions of formation-flying spacecraft, eigenstructure/manifold analysis of N-body dynamics, etc., when the exact structure-preserving property is crucial. We present the derivation and key characteristics of the symplectic state transition matrix and apply it to the two-body dynamics, the circular restricted three-body problem, and an Earth orbit with perturbation forces based on the real ephemeris. These numerical examples reveal that this numerical symplectic state transition matrix shows improvements in preserving the structural properties of the state transition matrix as compared with the conventional linear state transition matrix with Euler or Runge―Kutta integrations.