This information is part of the Modelica Standard Library maintained by the Modelica Association.
from_nxz
Return fixed orientation object from n_x and n_z vectors
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SOLUTIONS
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SOLUTIONS
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Return fixed orientation object from n_x and n_z vectors
It is assumed that the two input vectors n_x and n_z are resolved in frame 1 and are directed along the x and z axis of frame 2 (i.e., n_x and n_z are orthogonal to each other) The function returns the orientation object R to rotate from frame 1 to frame 2.
The function is robust in the sense that it returns always an orientation object R, even if n_z is not orthogonal to n_x. This is performed in the following way:
If n_x and n_z are not orthogonal to each other, first a unit vector e_z is determined that is orthogonal to n_x and is lying in the plane spanned by n_x and n_z. If n_x and n_z are parallel or nearly parallel to each other, a vector e_z is selected arbitrarily such that n_x and e_z are orthogonal to each other.