| Abstract: |
| We study the planar restricted 3-body problem (PR3BP). Although many numerical studies suggest the existence of transit orbits, few mathematical results have demonstrated their existence. For the case of two bodies in circular motion (PCR3BP), Moeckel (2005) provided a sufficient condition for their existence by minimizing Maupertuis` functional. However, in the case of elliptic motion (PER3BP), this variational structure does not apply because the system is non-autonomous, and no variational results had been known. We provide a different sufficient condition for PCR3BP by minimizing Lagrange`s functional without fixing time. Furthermore, we found that this variational structure is also applicable to non-autonomous systems, allowing us to establish a sufficient condition for PER3BP. We also numerically confirm that these sufficient conditions hold in specific cases where the two bodies have equal mass. In this talk, we will present these results. |
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