This paper proposed an analytical iterative guidance method with the desired instantaneous impact point constraint for solid rockets in “burn-coast-burn” trajectory mode. Solid rocket motors expect to remove the thrust termination mechanism to increase the structural strength and launch reliability, which induce new difficulties and challenges to the guidance problems. In terms of the “Hohmann transfer” principle, a pointing algorithm is deduced in depth to establish the theoretical relations among the ignition time, the required velocity vector, and the orbital element constraints and provides the analytical expression of the ignition time. Then, an analytic solution of the required velocity vector is derived based on orthogonal and nonorthogonal velocity vectors, and a complete guidance logic is used to solve the target orbit elements satisfying the desired instantaneous impact point. Finally, the application of the developed theoretical algorithm in this paper is conducted using a two-stage solid rocket. The proposed guidance method is verified by Monte Carlo simulations, and the testing results demonstrate the adaptability, strong robustness, and excellent performance for different desired impact point missions.

中文翻译：

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固体火箭用海岸弧的瞬时撞击点引导

本文提出了一种具有期望瞬时撞击点约束的固体火箭“燃烧-海岸-燃烧”轨迹模式的解析迭代制导方法。固体火箭发动机希望取消推力终止机构以增加结构强度和发射可靠性，这给制导问题带来了新的困难和挑战。根据“霍曼传递”原理，深入推导了指向算法，建立了点火时间、所需速度矢量和轨道元素约束之间的理论关系，并提供了点火时间的解析表达式。然后，基于正交和非正交速度向量推导出所需速度向量的解析解，并使用完整的制导逻辑来求解满足所需瞬时撞击点的目标轨道元素。最后，本文所开发的理论算法的应用是使用两级固体火箭进行的。所提出的制导方法通过蒙特卡洛模拟验证，测试结果证明了对不同期望落点任务的适应性、强大的鲁棒性和优异的性能。