# A Hopf variables view on the libration points dynamics

## TL;DR

This paper analytically investigates the dynamics near libration points in the Hill problem using Lissajous variables and perturbation theory, revealing the structure of invariant manifolds and limitations near libration energies.

## Contribution

It introduces a novel analytical approach employing Lissajous variables to simplify and analyze the Hill problem's libration point dynamics.

## Key findings

- Invariant manifolds structure is characterized.
- Method reduces problem to a one degree of freedom Hamiltonian.
- Computations are accurate near libration point energies.

## Abstract

The dynamics about the libration points of the Hill problem is investigated analytically. In particular, the use of Lissajous variables and perturbation theory allows to reduce the problem to a one degree of freedom Hamiltonian depending on two physical parameters. The invariant manifolds structure of the Hill problem is then disclosed, yet accurate computations are limited to energy values close to that of the libration points.