The formulas for the components of vectors and q} are identical. Points on the edges of the rings and are represented by the circumferences of radius , which are given by vectors or which depend on the parameters or , which vary from 0 to . The components of radius vector g7 in system of coordinates 3 are respectively equal to cos u; sin . Formulas for the components of vector 7 are identical. The segments may touch each other, giving six possible points of interaction the segments may touch the circumferences of the rings, with the possible formation of another 12 points of interaction and , and finally, the circumferences may touch the plane of the other ring, giving the last two points (. To find the points of interaction we introduce an auxiliary vector p(w), which depends on parameter w. For this vector lies in a plane parallel to the plane of the ring, and unites the point of intersection of segment with plane , which contains segment For and vector lies in the plane of the rings in the continuation of the radius of the ring to the point of intersection of the segment with the plane of the ring. In this case the components of the sum of vectors in system of coordinates 3 are respectively equal to where u varies from 0 to 2x. The formulas for the components of the sum of vectors q and p are analogous. For (Figure 4.4) vectors p are directed normal to the plane of the ring into the point on the circumference of the other ring, which is an extremely short distance away from it. When vector p turns to zero (parameter w in this
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