Rotor Kinematics

Remark 1.15. Clamped boundary conditions apply at the origin of the beam s 

the considered moving reference frame agrees with the coordinate system introduced to describe the beam. Therein the position of an arbitrary 

The position of the moving reference frame with respect to the rotating reference frame is given by the vector r, while its orientation is specified by the rotational transformation T32i(t). This may be assembled from the rotations around individual axes  

Since the Cardan angles asit), a2(i), and ai(t) are prescribed parameters, a discussion on the uniqueness of representation in analogy to Section 7.1.2 is not necessary and we may simply agree upon their sequence. The orientation of the rotating reference frame relative to the inertial reference frame is described by the rotational transformation 

For the sake of simplicity, the orientation of the inertial reference frame may be chosen such that one of its axes represents the axis of rotation. In the case of Eq. (7.67), the rotation occurs around the third axis of the inertial reference 

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By stirrer, we generally mean a moving system (consisting of a rotor equipped with blades) which, when rotating, produces in a reactor a mean flow and some turbulence. Such a device obviously differs from a static mixer, wherein a complex geometrical configuration of the reactor forces the flow to acquire kinematics that promotes the mixing of fluid particles. ... 

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