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Rotation: tibial internal rotation, expressed in degrees (deg).
Every rotation, expressed by its quaternion values, can then be approximated by a rotation around the vertical axis [0 0 ± 1] T or in aeronautics terms rotations are limited to yaw.
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Rotations were expressed as rotations about the x-axis (anterior/posterior), rotations about the y-axis (external/internal rotations), and rotations about the z-axis (adduction/abduction).
Excursion in one rotation cycle (from full external rotation to full internal rotation and back to full external rotation) was expressed as a percentage.
The resulting 4×4 transformation matrix was decomposed in a rotational and translation part: The residual rotation was expressed in axis-angle representation and additionally as three constitutive rotations (i.e., Euler rotations) [ 17] around a standardized coordinate system as depicted in Fig. 3.
The transverse displacement and local rotation are expressed as an infinite series.
Penetration rate can also be calculated on the basis of the distance excavated per cutter head rotation and expressed as an instantaneous penetration or as the average over each thrust cylinder cycle or other time periods listed above.
The angular rotation velocity for infinitely long non-neutral plasma column confined radially by a uniform magnetic field given by [4, 24] ω r e ± = Ω c e / 2 γ 1 ± 1 - 2 ω b 2 / Ω c e 2 1 / 2. In the presence of plasma or some positive ions laminar rotation frequency expressed by: ω r e ± = Ω c e / 2 γ 1 ± 1 - 2 ω b 2 / Ω c e 2 1 - f - β b 2 1 / 2. Here, f is the fractional charge neutralization.
The rotations were expressed about the transverse axis (x-axis, anteroposterior (AP) rotation), longitudinal axis (y-axis, internal-external rotation), and sagittal axis (z-axis, varus-valgus rotation) of the knee.
Rotations are expressed in terms of dorsopalmar tilt, radial inclination and axial rotation (pronation and supination).
The deviation from the actual rotation axis was expressed as rotational and translational error (±SD).
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