用欧拉角表示的飞行器姿态运动学方程在大角度时会出现奇异现象,而采用四元数来

表示,则可以避免这个问题。因此,飞行器运动学方程都采用四元数来表示。而飞行器的控

制规律都采用欧拉角来表示,且欧拉角表示姿态角比起四元数更加形象,更易于被人理解,

所以,在飞行器控制系统仿真设计的时候,需要四元数与欧拉角之间的转换。给定1 个欧拉

角,对应1 个四元数,因而欧拉角到四元数之间这种一一对应的关系使得欧拉角到四元数的

转换比较容易。但是,1 个四元数通常有1 个或者2 个欧拉角与之对应,它们之间不是一一

的对应关系,因而,四元数到欧拉角之间的转换比较困难。一般文献或者参考资料上的转换

仅仅适于欧拉角在- 90°～ + 90°之间的情况[1 ] 。文献[ 2 ,3 ]中给出了滚动轴在- 90°～ + 90°

之间变化,俯仰轴、偏航轴在- 180°～ + 180°之间变化的四元数到欧拉角的转换公式。本文

提出了滚动、俯仰和偏航3 个轴的欧拉角均在- 180°～ + 180°之间取值的全角度转换算法,

经过数字仿真证实,这个算法是完全正确的、而且很实用。-Euler angles of the spacecraft attitude kinematics equation at large angles appear strange phenomenon, and quaternion

, You can avoid this problem. Therefore, the aircraft kinematic equations using quaternion to represent. Aircraft control

The system of law Euler angles and Euler angles attitude angle than the the quaternion more image easier to be understood,

Therefore, in the design of aircraft control system simulation, you need to convert between quaternions and Euler angles. Given an Euler

Angle corresponding to a quaternion, which this one-to-one relationship between the Euler angles to quaternion makes Euler angles to quaternion

Conversion is relatively easy. However, a quaternion usually have one or two corresponding Euler angles between them than eleven

The correspondence relationship, therefore, the quaternion to convert between the Euler angle is relatively difficult. General literature or reference conversion

Only suitable for Euler angles- 90 ° to+ 90 ° betwe