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The current investigation presents the development of the proposed technique from a previous Lagrangian model, and consequently the mathematical relationships between the two coordinate sets are found.
As stated above, the rotor can be used to realize the rotation between the two coordinate systems.
There are six possibilities of rotating sequences (i.e., xyz, xzy, zxy, zyx, yzx, and yxz), and zxy is picked to construct the transformation matrix between the two coordinate systems (Equation 1).
An algorithm is then used to find the best transformation between the two coordinate systems using these two data sets.
After the calibration of the OTS system was complete, a static recording of the position of the RSA calibration cage was made to obtain the systematic difference between the two coordinate systems.
Although any point (x, y) ∈ ℝ should have a corresponding coordinate (s, t) C in the curvilinear coordinate system induced by C, closed-form expressions for converting between the two coordinate systems would be difficult or impossible to find.
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As described above, the analysis of the results in the frequency domain did not provide strong evidence for interactions between pursuit along the two coordinate axes in the sense that the phase of the responses generally did not depend on the target motion in the other dimension.
Bridging of the titanium atoms in an alkoxo-bridged dimeric Ti2 OR 4 unit (type A in Scheme 3) is only possible if the spacer between the two coordinating units is flexible enough to adjust to the Ti Ti distance in this unit, which is determined by the geometry of the central Ti2O2 ring.
5, 7 Especially, the class of bridging α,ω-bis tetrazol-1-yl)alkanes (nditz; n is the number of carbon atoms in the alkyl spacer) was of great interest,ω-bis tetrazol-1-ylion of the spacer length between the two coordinating tetrazole moieties created a fascinating playground for the investigation of the impact of the used solvent and the counteranion on the SCO behavior of the complexes.
In this Note, a configuration factor between a circle and the three coordinate directions is presented.
Following complex mathematical analysis, the authors have found exact expressions for the elusive configuration factor between a circle and the three coordinate axes.
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