Notice of Retraction: Attitude solution of vertical penetrative trajectory based on quaternion

In vertical penetrative trajectory, attitude solution will be singularity when pitch angle is -90deg, this paper take attention to study an omnidirectional space attitude solution method of vertical penetrative trajectory base on quaternion. Firstly, relations between quaternion transformation matrix and Euler angle transformation matrix are analyzed, then, omnidirectional space quaternion initialization method, quaternion update arithmetic and the method of Euler angles account from quaternion are studied. Secondly, the vertical penetrative trajectory simulation model based on quaternion is established to resolve the singularity problem of attitude solution in vertical penetrative trajectory based on Euler angle, the accurate omnidirectional space attitude solution is obtained. Finally, a series of vertical penetrative trajectory simulations demonstrate that the method is perfectly feasible and convince to be used in the attitude solution of vertical penetrative trajectory engineering design.