Eight Definitions for Spatial Rotations and Their Implications in the Second-Order Analysis of Space Frames

摘要

Although it is widely recognized by structural researchers that sequentialrotations about axes fixed in space are not commutative, there prevails confusion in the literature about different definitions of rotations and different rotational parameters employed in handling compound spatial rotations. Different definitions of rotations or different parameters have been referred to by the same name and vice versa, and computation algorithms that are valid for certain types of rotation have been applied indiscriminately. Some researchers misunderstand the relationships between rotations and moments in space, and others fail to grasp the implications of certain types of rotation in the second-order analysis of space frames. The present work describes eight definitions for spatial rotations and points out their implications in the second-order analysis of space frames subjected to conservative loads. A redefinition of semi-tangential rotations as vectorial rotations is also proposed.