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计算四元数的自然对数。Calculates the natural logarithm of a quaternion.

通过它，可以掌握四元数的一些特征。Through it, we can get quaternion some characteristics.

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用当前四元数的自然对数替换此四元数。Replaces the current quaternion with its natural logarithm.

答案在这，你首先需要计算你的四元数的平均值。To answer that, you first need to calculate the norm of your quaternion.

四元数的发现是数学史上的一个重大的事件。The discovery of quaternion is an importance event in the history of math.

在这方面，四元数的理论和方法或许是合适的。In this aspect, the quaternion theories and methods perhaps are appropriate.

本文讨论四元数矩阵右特征值的存在性问题。In this paper, we study the existence for right eigenvalue of quaternion matrix.

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本文获得了四元数矩阵的范数和迹的一些不等式，改进了近期的某些结果。In this paper, we obtain some inequalities for norm and traces of quaternion matrices.

四元数变换和矢量代数是本文中并联机构分析的理论工具。The unit quaternion transformation and vector algebra are applied to be analysis tools.

这是一个四元数。它定义关节可以旋转到的所需旋转角。This is a Quaternion. It defines the desired rotation that the joint should rotate into.

用四元数方法建立起卫星动力学方程和运动学方程。The satellite dynamics equation and kinematic equations are built with the method of quaternion.

四元数的W组件。不要直接修改这个，除非你很了解四元数。W component of the Quaternion. Don't modify this directly unless you know quaternions inside out.

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四元数的X组件。不要直接修改这个，除非你很了解四元数。X component of the Quaternion. Don't modify this directly unless you know quaternions inside out.

四元数的Y组件。不要直接修改这个，除非你很了解四元数。Y component of the Quaternion. Don't modify this directly unless you know quaternions inside out.

四元数的Z组件。不要直接修改这个，除非你很了解四元数。Z component of the Quaternion. Don't modify this directly unless you know quaternions inside out.

由此，把复数域上矩阵论的若干重要定理推广到了四元数体。Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.

应用四元数来描述姿态运动，以消除大角度机动飞行时欧拉角描述所存在的奇异性。The attitude dynamics is described by quaternion to eliminate singularity of Euler angle description.

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文章还讨论了四元数形式的矢量微分运算的一组计算公式。In addition, the paper also discussed a group of formula of vector differentiation in quaternion form.

基于四元数误差分析的方法，研究了导弹姿态扰动情况下全方位运动的误差问题。Errors of the omnidirectional attitude motion of missile were studied based on error quaternion method.

以四元数作为定位参数对空间站进行姿态控制。In this paper, the quaternion is taken for positional parameters to control attitude of the space station.