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On the commutativity of sequential finite rotations

机译：关于连续有限旋转的可交换性

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Non-commutativity of finite rotations is a fundamental issue that needs to be addressed in mathematical models dealing with sequential finite rotations. Comprehending rotational motions required to orient a rigid link or associated reference frames in a three-dimensional space can be quite challenging for beginning students. In this paper we present the problem of non-commutativity of finite rotations and a constraint to allow their commutativity. The constraint, in the form of a chain rule, consists of a lemma for forward and backward propagation of the prescribed rotations. The proposed scheme has been implemented using a commercial graphics package for visual demonstration of a rigid body going through three identical finite rotations but in different sequences. The unique final orientation of the body in each of the cases confirms the commutative nature of the constrained rotations. Using this method, sequential finite rotation becomes easy to comprehend and can be used as a tool for learning the concepts associated with finite rotations as well as for kinematical analysis involving sequential rotations.
机译：有限旋转的不可交换性是一个基本问题，在处理顺序有限旋转的数学模型中需要解决。对于初学者来说，理解在三维空间中定向刚性链接或相关参考框架所需的旋转运动可能会非常困难。在本文中，我们提出了有限旋转的非可交换性问题以及允许其可交换性的约束。约束采用链式规则的形式，由一个使指定旋转向前和向后传播的引理组成。所提议的方案已使用商业图形包实现，以视觉方式展示刚体经过三个相同的有限旋转，但顺序不同。在每种情况下，物体独特的最终取向都证实了约束旋转的可交换性质。使用这种方法，顺序有限旋转变得容易理解，并且可以用作学习与有限旋转相关的概念以及涉及顺序旋转的运动学分析的工具。

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