论文标题
欧拉旋转定理的替代证明
An alternative proof for Euler rotation theorem
论文作者
论文摘要
Euler的旋转定理指出，具有固定点之一的刚体的任何重新配置等同于围绕通过固定点的轴的单个旋转。定理构成了Chasles定理的基础，该定理指出，始终可以通过翻译和围绕轴的旋转来表示刚体的一般位移。尽管有很多方法可以实现这一目标，但是旋转轴和旋转角的方向与翻译矢量无关。该定理在研究刚体动力学的研究中很重要。这些定理有各种证据，包括几何和代数。这里给出了一个新颖的Euler旋转定理的几何证明，它利用大约两个相互垂直轴的两个连续旋转，从一个刚体的一种构型到另一个构型，其一个点固定。
Euler's rotation theorem states that any reconfiguration of a rigid body with one of its points fixed is equivalent to a single rotation about an axis passing through the fixed point. The theorem forms the basis for Chasles' theorem which states that it is always possible to represent the general displacement of a rigid body by a translation and a rotation about an axis. Though there are many ways to achieve this, the direction of the rotation axis and angle of rotation are independent of the translation vector. The theorem is important in the study of rigid body dynamics. There are various proofs available for these theorems, both geometric and algebraic. A novel geometric proof of Euler rotation theorem is presented here which makes use of two successive rotations about two mutually perpendicular axis to go from one configuration of the rigid body to the other with one of its points fixed.
