摘要
空空导弹的运动方程通常用一组基于欧拉角的微分方程来表示,但欧拉角方程有时具有奇异性,会使得微分方程不可求解,而采用四元数法则可以有效克服这一问题。本文以现有基于欧拉角的空空导弹六自由度数学模型为基础,用导弹各个坐标系之间的转换关系以及四元数来表示刚体的平移和转动,把已知的欧拉角导弹模型转换为四元数导弹模型。以样例导弹为对象,分别将欧拉角模型和四元数法模型在Matlab环境下进行了仿真,结果表明四元数法模型与欧拉角模型的仿真结果一致,并且四元数法模型具有更快的运行速度。
The equation of motion of air-to-air missile is usually represented by a set of differential equations of Euler angles. Euler angle has a singularity equations, differential equations can not be solved sometimes, while the use of quaternion can overcome this problem. In this paper, the Euler angles of the existing missile 6dof mathematical model is used to convert between various coordinate systems and missile quaternion to represent the translational and rotational rigid body, the missile model of Euler angles can be converted to quaternion missile model. To an sample missile model, the Euler angle mode and quaternion model were both simulated in matlab environment, simulation results show that the quaternion model and the Euler angle model have the same outputs and quaternion model with faster speed.
出处
《科技信息》
2014年第7期51-52,共2页
Science & Technology Information
关键词
空对空导弹
四元数
数学模型
建模
Air-to-air missile
Quaternion
Mathematical model
Modeling
