Simultaneous Orthogonal Rotations Angle
Simultaneous Orthogonal Rotations Angle
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同时正交旋转角度
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
in
中科院分区：
文献类型：
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作者：
Sašo Tomaži;Sara Stan;in
角取向是指刚体固有坐标系相对于具有相同原点的参考坐标系的位置。它是通过将最初与参考坐标系轴对齐的刚体坐标系轴移动到其新位置所需的旋转序列来确定的。在本文中，我们提出了一种新的方法来表示角取向。我们定义了同时正交旋转角（索拉）矢量，其分量等于围绕坐标系轴的三个同时旋转的角度。这里避免了不可交换性的问题。我们数值验证了索拉等于旋转矢量-它包含的三个同时旋转相当于一个旋转。该旋转的轴与索拉矢量重合，而旋转角度等于其大小。我们进一步验证，如果坐标系最初对齐，同时旋转的参考和刚体的内在轴表示相同的角取向。考虑到索拉矢量，可以在一个步骤中计算刚体的角取向，从而避免了迭代的无穷小旋转近似计算。因此，索拉可以是一个非常方便的角度取向表示的方式。
Angular orientation refers to the position of a rigid body intrinsic coordinate system relative to a reference coordinate system with the same origin. It is determined with a sequence of rotations needed to move the rigid-body coordinate-system axes initially aligned with the reference coordinate-system axes to their new position. In this paper we present a novel way for representing angular orientation. We define the Simultaneous Orthogonal Rotations Angle (SORA) vector with components equal to the angles of three simultaneous rotations around the coordinate-system axes. The problem of non-commutativity is here avoided. We numerically verify that SORA is equal to the rotation vector – the three simultaneous rotations it comprises are equivalent to a single rotation. The axis of this rotation coincides with the SORA vector while the rotation angle is equal to its magnitude. We further verify that if the coordinate systems are initially aligned, simultaneous rotations around the reference and rigid-body intrinsic axes represent the same angular orientation. Considering the SORA vector, angular orientation of a rigid body can be calculated in a single step thus avoiding the iterative infinitesimal rotation approximation computation. SORA can thus be a very convenient way for angular-orientation representation.