Circular trajectory guidance law with impact angle constraint based on PNG

The theorem is proved that the missile trajectory is a circular curve, when the initial guidance condition is satisfied that the difference between line-of-sight angle and trajectory inclination angle is equal to the difference between desired impact angle and line-of-sight angle, and then the proportional navigation guidance (PNG) whose navigation coefficient equals 2 is executed to attack the stationary target. Based on this theorem, a circular trajectory guidance (CTG) law with impact angle constraint is proposed, and the fixed rudder angle method is used to reach the initial guidance condition. The guidance law is used to the guided artillery rocket with limited maneuverability and ballistic trajectory. Simulation results show that the rocket can hit the target at desired impact angle, and the required lateral overloads during guidance phase is relatively small and it match very well with the available lateral overloads.