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According to Minkowski's reformulation of special relativity, a Lorentz transformation may be thought of as a generalized rotation of points of Minkowski space-time into themselves.
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According to Wertz research, if it is assumed that point A does not move forward during rapid maxillary expansion, the change in the ANB angle could be a result of posterior rotation of point B [23].
Now it seems we have a paradox, since the mapping that consists of a rotation of all points in a circular state-space by 90 degrees does not have a fixed point.
The Procrustes results reflect that differences between ascertainment scheme affect rotation of the points relative to the axes, rather than relative to the other sampled individuals.
Open image in new window Fig. 5 Normalized true stress vs. angle for rotation of the point Y: α = π/2.
One can alternatively use a Cholesky decomposition, but as noted by Jäckel (2005), the spectral decomposition provides a better rotation of the sampling points, which makes the evaluation of the integral potentially more robust.
In the present study this will result in a relative rotation of tibiofemoral contact points at 120° KFA of 21.8° or 22° as a rounded value.
The results determined by Iwaki et al. [ 13] in a cadaveric study on 6 knees show a relative rotation of tibiofemoral contact points around a medial pivot (mean MP ± 1.5 mm) of 22.4° at 120° KFA [ 13].
Their position is influenced by two design parameters the scaling parameter determining the spread of the σ-points and a covariance matrix decomposition determining rotation of the σ-points.
Now, consider the counterparts in rotational motion: angular displacement, θ, the angle of the rotation of a certain point or line (SI unit: rad); the angular velocity, ω, time rate change of angular displacement (SI unit: rad/s); and the angular acceleration, α, the change in angular velocity per unit time (SI unit: rad/s2).
The first energetic force is shown to be given by the product of the force and the rotation of the loading point.
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