基于几何关系的刚体姿态描述矩阵的导出与解析

Derivation and Analysis of Description Matrix for Rigid Body Attitude Based on Geometric Relationship

从两直角坐标系各坐标轴间的几何关系入手,组合排列出刚体姿态描述矩阵的一般式,利用向量点积性质及刚体姿态描述矩阵的一般式推导出坐标旋转方程,进一步应用刚体姿态描述矩阵的一般式,借助两坐标系各坐标轴间几何关系,得出描述刚体姿态的三个基本旋转矩阵的具体形式;利用两坐标系的几何关系,借助辅助坐标系推导出描述刚体姿态的旋转通式,并由旋转通式得出描述刚体姿态的三个基本旋转矩阵的具体形式。

Starting from the geometric relationship of axes in two rectangular coordinate systems,the general form of the description matrix for rigid body attitude was obtained through permutation and combination,which was then used to derive the coordinate rota⁃tion equation based on the property of vector dot product.Further,applying the general form of the description matrix for rigid body attitude,and with the aid of the geometric relationship of axes in the two coordinate systems,the specific form of three basic rota⁃tion matrixes describing rigid body attitude was obtained.Also,by using the geometric relationship between the two coordinate sys⁃tems and the auxiliary coordinate system,the general expression of rotation describing rigid body attitude was derived,which was then used to obtain the concrete form of the three basic rotation matrixes that describe rigid body attitude.