This paper presents a new method named "Analytic Orthogonalization", for orthogonalizing direction cosine matrix.

本文提出方向余弦矩阵正交化的一种新方法——解析正交化。

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Methods of spherical trigonometry and direction cosine matrix were applied respectively to derive the bracket error, and the two methods had the same error formula and the same calculation results.

应用球面三角法和方向余弦矩阵法分别推导出双轴陀螺平台的支架误差公式，发现由这两种方法推导出来的公式计算结果是一致的。

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The coordinate transformation matrix based on the direction cosine parameters from the object coordinate system to the world coordinate system is derived by vector algebra.

利用矢量代数的方法，推导出以方向余弦为参量的物坐标系到世界坐标系的坐标变换矩阵；利用矩阵求逆的方法，推导出世界坐标系到物坐标系的坐标变换矩阵。

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