基于变分迭代的航天器相对姿轨耦合动力学解算方法

针对航天器相对姿轨耦合一体化运动，在定义坐标系下利用对偶四元数和旋量表示航天器的一般运动，推导出航天器六自由度运动学和动力学模型，并分别采用Runge-Kutta四阶算法和变分迭代法的配点形式求解该非线性模型。变分迭代法的配点形式是变分迭代法与配点法的复合，本文先给出变分迭代法的迭代方程，再把迭代方程应用到局部时间区间上探讨了局部变分迭代法，然后把变分迭代法与配点法结合得到数值迭代方程。利用对偶四元数所建立的模型相对于其他模型较为简洁，便于分析姿轨耦合特性。仿真结果表明，相比Runge-Kutta四阶算法，变分迭代法的解算精度更高。

Calculation Method of Orbit-Attitude Coupling Dynamics for Spacecraft Relative Motion Based on Variational Iteration

The general relative motion of the spacecraft is represented by the dual quaternion and spinor in the defined coordinate system, and a six-degree-of-freedom kinematic and dynamical model of the spacecraft is derived. The nonlinear model is solved by adopting the Runge-Kutta fourth-order algorithm and the local variational iteration method (LVIM), respectively. The collocation form of the local variational iteration method is the compound of the local variational iteration method and the collocation method. In this paper, the iterative equation of the local variational iteration method is firstly given, and then the local variational iteration method is extended to a small-time interval, and finally the numerical iteration equation is obtained by combining the collocation method. Compared with other models, the model based on dual quaternion is simpler, which is convenient to analyze the coupling characteristics of attitude and orbit. The numerical results verify that the variational iteration method in collocation form is more accurate than the Runge-Kutta fourth-order algorithm.