2+2-Moulton Configuration - rigid and flexible

摘要

We consider a new problem on Moulton configuration. For a given two-body system, we add two bodies in a way such that (i) the total four-body system is also in a state of collinear central configuration without changing the positions of original two bodies and (ii) the initial two-body system keeps its motion without any change during the process. We show the existence of this configurations in a general way. We also pose a flexible version of this problem by modifying the condition (ii) and we also find solutions to the second problem.