Rotation calculation via quaternions has come to replace the use of direction cosines in aerospace applications through their reduction of the required calculations, and their ability to minimize round-off errors.
22.
These segments were used for computations that needed to be recalculated every 20 ms ( like IMU signal processing, update of PGNCS downlink data, direction cosines update, etc . ).
23.
The error signals are commonly measured as euler angles ( ?, ?, ? ), however an alternative to this could be described in terms of direction cosine matrix or error quaternion s.
24.
Where \ \ alpha _ { Ji } are the direction cosines between the material and spatial coordinate systems with unit vectors \ \ mathbf E _ J and \ mathbf e _ i, respectively.
25.
It is common to superimpose the coordinate systems for the undeformed and deformed configurations, which results in \ \ mathbf b = 0, and the direction cosines become Kronecker deltas, i . e.
26.
If the orientations are specified in terms of matrices of direction cosines g A and g B, then the misorientation operator " g AB going from A to B can be defined as follows:
27.
Consider the electric field at two points, P _ 1 and P _ 2, in the detection plane due to some point in the source whose coordinates are given by the direction cosines l and m
28.
It is common to superimpose the coordinate systems for the deformed and undeformed configurations, which results in \ mathbf b = 0 \, \ !, and the direction cosines become Kronecker deltas, i . e.
29.
I know how to extract the maximum shear stress ( 0.5 * ( sigma1-sigma3 ) ), but what I really need are the direction cosines to go from A to that tensor where that maximum shear stress exists.
30.
However, in practice, \ vec { r } _ 1, \ vec { r } _ 2 are noisy and the orthogonality condition of the attitude matrix ( or the direction cosine matrix ) is not preserved by the above procedure.
