The two-boost problem and the boundedness of Reeb chords

TL;DR

This paper investigates the two-boost problem in space mission design, establishing conditions under which two points can be connected by a Hamiltonian path on a fixed energy level, using Floer homology techniques.

Contribution

It introduces a novel approach linking the two-boost problem to Lagrangian Rabinowitz Floer homology and proves boundedness of Reeb chords for certain systems.

Findings

Positive solution for the two-boost problem in specific systems

Connection between Hamiltonian paths and Floer homology methods

Boundedness of Reeb chords established for the class of systems studied

Abstract

The two-boost problem in space mission design asks whether two points of position space can be connected by a Hamiltonian path on a fixed energy level set. We provide a positive answer for a class of systems having the same behaviour at infinity as the restricted three-body problem by relating it to the Lagrangian Rabinowitz Floer homology computed in [4]. The main technical challenge is to prove the boundedness of the corresponding sets of Reeb chords.