부산대학교 도서관

In this paper the author considers a planar symmetric four-body problemcalled the {\it rhomboidal symmetric four-body problem}. This problemconsists in considering two equal point masses $m_1=m_3>0$ placed at$(\pm x_1(t),0)$ in a fixed plane (described by Cartesian coordinates$x,y$) and two equal masses $m_2=m_4>0$ at positions $(0,\pm y_2(t))$.Provided that the initial velocities are chosen in order to satisfythis symmetry, the rhomboidal nature of the constellation is preservedalong the motion.\parIn spite of the simplicity of the equations of motion this problem isvery interesting from the dynamical point of view because it iscomplicated enough to show the presence of binary collisions, periodicsolutions and homothetic solutions at central configurations. Amongother things the role of resonance phenomena between the twointeracting rectilinear binaries for generating periodic orbits isstudied, and the McGehee regularization is worked out.