具有扁体的Hill四体问题的正则化
Regularization of the Hill four-body problem with oblate bodies
摘要：
我们考虑希尔四体问题，其中三个扁，大规模的机构形成一个相对平衡的三角形配置，和第四，无穷小的机构轨道附近的最小的三个大规模的机构。通过McGehee坐标变换，我们正则化了无限小物体和最小质量物体之间的碰撞。我们描述了相应的碰撞流形，并表明，它经历了一个分支时，小质量体的扁率系数通过零值。
英文摘要：
We consider the Hill four-body problem where three oblate, massive bodies form a relative equilibrium triangular configuration, and the fourth, infinitesimal body orbits in a neighborhood of the smallest of the three massive bodies. We regularize collisions between the infinitesimal body and the smallest massive body, via McGehee coordinate transformation. We describe the corresponding collision manifold and show that it undergoes a bifurcation when the oblateness coefficient of the small massive body passes through the zero value.
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