# Rotation of an oblate satellite: Chaos control

## TL;DR

This paper explores controlling chaotic rotation of an oblate satellite by applying a small additive control term, transforming chaotic motion into periodic motion using Hamiltonian formalism.

## Contribution

It introduces a novel control method that suppresses chaos in satellite rotation with minimal energy input, based on the Beletskii equation and Hamiltonian approach.

## Key findings

- Control term effectively reduces phase space diffusion.
- Chaotic motion is converted into strictly periodic motion.
- Control method requires an order of magnitude smaller energy than the potential.

## Abstract

Aims. This paper investigates the chaotic rotation of an oblate satellite in the context of chaos control. Methods. A model of planar oscillations, described with the Beletskii equation, was investigated. The Hamiltonian formalism was utilized to employ a control method for suppressing chaos. Results. An additive control term, which is an order of magnitude smaller than the potential, is constructed. This allows not only for significantly diminished diffusion of the trajectory in the phase space, but turns the purely chaotic motion into strictly periodic motion.