论文标题
关于RSA总旋转的代数定义
On the algebraic definition of total rotation in RSA
论文作者
论文摘要
总旋转是在RSA中多年使用的数量。但是，它的定义没有数学意义，因为欧拉角并未形成向量空间，因为角度无法定义乘法组。通过这项工作，我试图对将旋转的欧拉描述与螺旋轴连接的总旋转进行数学定义。小角度的近似值用于连接欧拉的角度和螺旋角。有了这个近似值，欧拉角将获得矢量空间的属性，并且有可能证明此参数的含义是合理的。验证测试表明，在$ \ left [ - \fracπ{6}，\fracπ{6} \ right] $的范围内，总旋转的角度在5 \％和7％之间的近似误差。由于RSA通常使用较小的角度范围，因此近似非常适合在RSA中使用。
Total rotation is a quantity that has been used for years in RSA. However, its definition has no mathematical sense, since the Euler angles do not form a vector space, since angles cannot define a multiplication group. With this work I tried to give a mathematical definition of the total rotation connecting the Euler description of the rotations with the helical axis. The approximation for small angles was used to connect Euler's angles and helical angle. With this approximation Euler angles acquire the properties of a vector space and it is possible to justify the meaning of this parameter. Validation test showed that total rotation has an approximation error between 5\% and 7\% for angles in the range $\left[-\fracπ{6}, \fracπ{6} \right]$. Since usually RSA uses smaller angle ranges, the approximation is perfectly suitable for use in RSA.
