# A note on the geometric modeling of the full two body problem

## TL;DR

This paper derives the equations of motion for two interacting rigid bodies using geometric mechanics, providing a mathematical framework for understanding their complex gravitational dynamics.

## Contribution

It introduces a geometric mechanics approach to formulate the Euler-Poincare and Hamiltonian equations for the full two-body problem.

## Key findings

- Derived Euler-Poincare equations for the two-body problem
- Formulated Hamiltonian equations using geometric mechanics
- Provides a mathematical foundation for future analysis of rigid body interactions

## Abstract

The two full body problem concerns the dynamics of two spatially extended rigid bodies (e.g. rocky asteroids) subject to mutual gravitational interaction. In this note we deduce the Euler-Poincare and Hamiltonian equations of motion using the geometric mechanics formalism.