Abstract

The purpose of the present paper is to investigate the motion’s properties of an infinitesimal body in three-dimensional version of Hill’s problem where the mass of the infinitesimal body is supposed to vary with time. As commonly done, the infinitesimal body is assumed to move under the influence of the other massive and oblate bodies that also have radiation effects. We suppose that the whole system is subject to a perturbation on Coriolis and on centrifugal forces. By using the various transformations, we extract the equations of motion and Jacobi quasi-integral. The properties like the locations of equilibrium points, regions of motion, surfaces with projection, trajectories allocation and the basins of attraction are investigated for various values of mass parameters. The stability is examined by using Meshcherskii space-time inverse transformations.

中文翻译：

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变质量希尔问题的三维版本

摘要

本文的目的是在希尔问题的三维版本中研究无穷小物体的运动特性，其中假设无穷小物体的质量随时间变化。正如通常所做的那样，假设无穷小的物体在其他同样具有辐射效应的大质量和扁球体的影响下移动。我们假设整个系统受到科里奥利和离心力的扰动。通过使用各种变换，我们提取了运动方程和雅可比拟积分方程。对于各种质量参数值，研究了平衡点的位置、运动区域、带投影的表面、轨迹分配和吸引盆等特性。