부산대학교 도서관

In this paper the author considers a planar symmetric four-body problem called the {\it rhomboidal symmetric four-body problem}. This problem consists 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 satisfy this symmetry, the rhomboidal nature of the constellation is preserved along the motion. \par In spite of the simplicity of the equations of motion this problem is very interesting from the dynamical point of view because it is complicated enough to show the presence of binary collisions, periodic solutions and homothetic solutions at central configurations. Among other things the role of resonance phenomena between the two interacting rectilinear binaries for generating periodic orbits is studied, and the McGehee regularization is worked out.