Sentence examples for with respect to the rotation from inspiring English sources

The pore mass center with position vector p is rotated with an angle ω around the z-axis with respect to the rotation point (R x,R y,0).

Note that we assume axisymmetry with respect to the rotation axis; thus, the dust density is independent of y.

The phase-averaged flow fields with respect to the rotation angle of the turbines revealed two types of power-improvement interactions.

It is found that the L CR) is an invariant with respect to the rotation of coordinates, and it has a variation when the coordinates have a translation.

We define the objective function F with respect to the rotation matrix Q for the manifold optimization as follows begin{array}{*{20}l} F(mathbf{Q}) = mathbb{E}left[Vert mathbf{p} - boldsymbol{Pi}mathbf{Q}(bar{mathbf{s}} + mathbf{V}mathbf{z}) {Vert_{F}^{2}}right]. end{array} (13).

Compared to the conventional V-blender, this geometry is shown to provide shorter mixing times and better axial and radial mixing efficiency, especially when its upper or lower V-shaped part is twisted by 45° with respect to the rotation axis.

The hip rotation demonstrated the smaller absolute angles with respect to the pelvic rotation.

In this case, transforming the local coordinate into the global one is equivalent to imposing the transposition/inversion with respect to the above rotation matrix.

where W i is the multiplier and ρ is the mass density andz′ is the position of the layer with respect to the axisof rotation.

As such, friction stir welding of overlap joints was carried out on 2 mm thick sheets, where the orientation of the pull direction of the coupon was varied with respect to the tool rotation direction.

The stiffness of the elastic foundation can be different in the vertical and horizontal planes, thereby considering the anisotropy of the engine block compliance with respect to the crankshaft rotation.