This paper proposes a numerical method to solve the two-target interception problem with a single impulse. Free impulse position and free interception position are considered. Both elliptic and hyperbolic transfers are analyzed. Under the two-body model, by using the Gibbs method for orbit determination from three position vectors, the problem is transformed into solving nonlinear equations of only two independent variables. Newton-Raphson iterations associated with analytical Jacobi matrix are adopted to solve the nonlinear equations. The initial guesses are obtained by the Porkchop plot method. By using the solutions under the two-body model as the initial values, the solutions under the $J_2$-perturbed model are obtained by combining the homotopy technique and the differential correction method. There are many solutions for the problem even for the zero-revolution case. Numerical examples are provided to verify the effectiveness of the proposed methods for the two-body model and the $J_2$-perturbed model, respectively.

本文提出了一种求解单脉冲双目标拦截问题的数值方法。考虑自由脉冲位置和自由拦截位置。分析了椭圆和双曲线传输。在二体模型下，利用吉布斯方法从三个位置向量确定轨道，将问题转化为求解只有两个自变量的非线性方程。采用与解析雅可比矩阵相关联的 Newton-Raphson 迭代来求解非线性方程。最初的猜测是通过 Porkchop plot 方法获得的。以二体模型下的解为初始值，得到$J_2$-摄动模型是通过结合同伦技术和微分校正方法获得的。即使对于零转情况，这个问题也有很多解决方案。提供了数值例子来验证所提出的方法对二体模型和$J_2$-扰动模型，分别。