Representing Attitude : Euler Angles , Unit Quaternions , and Rotation Vectors
Representing Attitude : Euler Angles , Unit Quaternions , and Rotation Vectors
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发表时间：
2006
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通讯作者：
J. Diebel
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作者：
J. Diebel
我们提出了三个主要的数学构造用于表示在三维空间中的刚体的姿态。它们是（1）旋转矩阵，（2）欧拉角的三元组，以及（3）单位四元数。在这些基础上，我们再加上第四个，旋转矢量，它具有欧拉角和四元数的许多优点，但既没有前者的奇点，也没有后者的二次约束。还有其他几个辅助表示，如凯莱-克莱因参数和轴角表示，其关系的三个主要表示也进行了说明。我们的论述是迎合那些谁寻求一个彻底的和统一的参考对整个主题;详细推导的一些结果没有提出。关键词-欧拉角、四元数、欧拉-罗德里格斯参数、凯莱-克莱因参数、旋转矩阵、方向余弦矩阵、变换矩阵、卡丹角、泰特-布赖恩角、航海角、旋转矢量、方位、姿态、横摇、俯仰、偏航、倾斜、航向、自旋、章动、进动、Slerp
We present the three main mathematical constructs used to represent the attitude of a rigid body in threedimensional space. These are (1) the rotation matrix, (2) a triple of Euler angles, and (3) the unit quaternion. To these we add a fourth, the rotation vector, which has many of the benefits of both Euler angles and quaternions, but neither the singularities of the former, nor the quadratic constraint of the latter. There are several other subsidiary representations, such as Cayley-Klein parameters and the axis-angle representation, whose relations to the three main representations are also described. Our exposition is catered to those who seek a thorough and unified reference on the whole subject; detailed derivations of some results are not presented. Keywords–Euler angles, quaternion, Euler-Rodrigues parameters, Cayley-Klein parameters, rotation matrix, direction cosine matrix, transformation matrix, Cardan angles, Tait-Bryan angles, nautical angles, rotation vector, orientation, attitude, roll, pitch, yaw, bank, heading, spin, nutation, precession, Slerp