运用皮欧符号法推导方向余弦矩阵的方法

The Method of Deducing Direction-cosine Matrix Using Piosymbolic

皮欧符号法是一种进行坐标变换的类似信号流图的方法,它提供了描述直角坐标系间方位关系的符号化表达形式,为飞行器等的导航算法设计工作提供便利。本文介绍了惯常的用于推导坐标变换的方向余弦矩阵的矩阵连乘方法,以实例对比介绍了如何用皮欧符号法推导方向余弦矩阵,总结了皮欧符号法变换图的绘制方法和利用皮欧符号图直接书写展开形式的方向余弦矩阵的规则,最后以几个常用的坐标变换为例说明了该方法给推导方向余弦矩阵带来的灵活性。

Pio-symbolic method is applied to transform coordinate similarly to signal flow chart,it describes the form of directions relation between cartesian coordinate systems essentially, offers convenience for designing navigation algorithm for aircraft. This paper introduces the matrix-by-matrix method that is usually used to deduce direction-cosine matrix and the instances of deducing direction-cosine matrix by Pio-symbolic method, summarizes the drawing method of pio-symbolic chart and the rule writing the expressions of direction-cosine matrix directly by pio-symbolic method. Finally the flexibleness of the method in deducing direction-cosine matrix is described by some examples of common coordinate transformation.