The
radius vector of the point N on the surface of the oscillating scatterer-pendulum hemisphere in the [O.sub.3][X.sub.3][Y.sub.3][Z.sub.3] coordinate system:
The speed vector is determined by the given angular speed of the rotor [[omega].sub.R] and the
radius vector of the current rotor point v = [[omega].sub.R]r.
One of the ground concepts used in statistical analysis of random structures and also applied in this work is based on perturbation approach [4, 16, 22, 23] and presumes that local stress and strain fields as well as local stiffness tensor depend on position of the
radius vector and can be decomposed into an averaged value and random addition:
It should be noted that we consider the special case when the spatial orientation of the coordinate axes of the laboratory coordinate system "L" and "L'" is the same, as well as the
radius vector of the start of the laboratory coordinate system "L'" in the laboratory coordinate system "L" coincides with the
radius vector of the moderating medium nucleus, at which the neutron scattering in the laboratory coordinate system "L" (that is the moderating medium nucleus in the laboratory frame "L'") is at rest.
Here r is the distance of the ghost galaxy to the Milky Way (the Milky Way being located at the focus of the orbit), p is the distance of closest approach (impact parameter), e is the eccentricity of the orbit, [theta] is the angle of
radius vector with respect to the x axis, and [v.sub.r], [v.sub.[theta]] are the parallel and perpendicular components of the velocity with respect to the radial position vector.
The problems of data harmonization for index convolution purpose were solved by using the logistic normalization and Euclidean norm for the
radius vector (3):
The figure illustrates a sharp crack and we have positioned a coordinate system at the crack tip showing the
radius vector r giving the direction and distance from the crack tip to any point in the material.
R is the length of [??], the
radius vector from the instantaneous position of the charge to the point of observation; [??] is the angle between [??][DELTA]t, the direction of motion of charge q, and [??].
In general, the virtual displacement of the moving platform of Hauff manipulator equals to the total differential of the
radius vector respect to the generalized coordinates:
Notice that we also use the module of the
radius vector because good parallax data are available.