To answer these questions, a numerical experiment was done. The equation of the motion (16) with the assumed constant values (19) were integrated within the time interval T = 1 year. The following initial condition were chosen: a sphere was built around the point Lj and Nj points were chosen at random inside this sphere. The sphere radius is (i is the variant number). The initial velocities were assumed to equal to zero. For q = 0.8 two variants are evaluated: The integration was made by the Gill's method with automatic step choice. The question about the numerical solution errors is of great importance. To solve it, our equation (16) were integrated for the particle which is situated exactly in the center of libration Lj. The particle deflection from it's original position due to the solution errors after 1 year period was found to be IO"16 AU, i.e. less then rj = 6-10‘10 AU by the factor 106. So the calculating errors have nearly no influence on the results. The projection of the final particles positions onto the plane XOY in the case 2 are shown in figure 1, where the coordinates frame with the center in the point Lj was used. The axes and Ljq being parallel to the axis OX and OY accordingly. The initial sphere is shaded. The following properties of the particles motion were established: 1. It is the extremely slight approach of the particles to the plane XOY both from the region with z > 0 and from the region with z < 0 . The distribution of the final positions to z- coordinate coincide with its initial distribution. 2. The scattering of the particles on the axis X is small too and doesn't surpass 2-3 times. 3. The dust particles experience the biggest displacement in the Y-direction (see figure 1). 4. If the initial particles position satisfies the condition t=0 < 0, this motion occurs in the direction of the increasing of q and decreasing of c, . Otherwise, if ^|f=0 > 0 then the coordinate c, will increase with time and T| will decrease. There are very rare exceptions from this rule (see figure 2c). In the first case (q = 102 m) the final positions configuration is the same but all the distances are approximately 2 factors less.
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