% Initialization Set the values for the parameters [omega], [c.sub.1], [c.sub.2] and Itr; Randomly initialize the position vector
[Pos.sup.0.sub.i] for each particle i, for i = 1,2, ...
Thus, the first input parameter of the NN is found by subtracting the measured position vector
from the estimated position vectors
for all positions.
From equations (9) & (10) each potential solution is represented as a particle with a position vector
and a moving velocity represented as w and v respectively.
In the EMA, a candidate solution is associated with a charged particle in a multidimensional space using a realcoded position vector
where r is the position vector
directed from the center of the line segment to the observation point.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the position vector
of the pack CoM relative to the trunk CoM, [??] is the pack translation relative to the trunk, and [??] is the position of the pack CoM, relative to the trunk CoM, in the unloaded condition.
[X.sub.i] represents the position vector
of particle i, R is a Random number between -1 and +1, [w.sub.i] is a vector pointing the direction of the line joining the point "i" and [x.sub.Global] and with size [absolute value of w] = (domain size)/(number of particles).
Consider a position vector
for CERN in relation to the center of the Earth, vector [??], and a position vector
for the Gran Sasso receptors in relation to the center of the earth, vector [??].
Satellite position vector
is denoted by [r.sub.P] = ([r.sub.P],[[alpha].sub.P], [[theta].sub.P]) in spherical coordinates, where aP and 9P can be calculated according to (4)
The position vector
r points from the origin of the coordinate system to a chosen point along the yarn, [rho] is the linear density of the yam mass, [omega] is the angular velocity vector of the spinning coordinate system in which the yarn is being described and which points along the z-axis, D is the operator of the total time derivative which follows the motion of the point inside the spinning coordinate system, D = [partial derivative]/[partial derivative]t|.sub.r,[theta],z] - V [partial derivative]/[partial derivative]s, T is the mechanical tension, f is the linear density of external forces.
In view of some special solutions of mentioned system, position vector
of rectifying curves, osculating curves with constant first curvature, normal curves and special cases are presented.
[X.sub.c] = Position vector
of a surface point at the exit of the channel at X = [X.sub.0].