Rigid Body Motion
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Extracting the properties of rigid body motion from everyday experience has taken mankind several hundreds of years. The major reason is that motions of rigid bodies obey fundamentally different properties than motions of points, i.e., the structure of rigid body motion is that of a curved space. There is one very important complication about rigid bodies that makes them a bit more tedious than points in the Euclidian, three-dimensional space (denoted E³): the geometry of rigid body motion is the geometry of frames in E³, since the pose (i.e., position and orientation) of a rigid body is uniquely defined by the pose of a reference frame attached to the rigid body. This space of frames does not have the geometry of the familiar Euclidean space, mainly due to the fact that rotations and translations do not commute, i.e., executing a translation first and then a rotation yields a different motion than executing the rotation first.
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