Planar vibrations of a solid with variable mass distribution in an elliptic orbit

摘要

Planar vibrations of a solid with variable mass distribution in an elliptic orbit is studied by considering the motion of a solid with a variable mass distribution in the central Newtonian field of forces with the center at a fixed point. The principal central axes of inertia of the solid are considered so that the inertia-tensor matrix has the diagonal form. At relative equilibriums, the solid is oriented so that one of axes is directed respectively either from the attracting center or towards it. The results of the numerical analysis of stability show that the boundary of the instability region corresponds to the case of stability. Because of splitting separatrices, the nonintegrability follows finite values of eccentricity instead of only small ones.