# The Lie-Trotter integrator in the dynamics of the symmetric free rigid body

## TL;DR

This paper demonstrates that the Lie-Trotter integrator acts as a Poisson integrator when applied to the Euler equations of a symmetric free rigid body, highlighting its importance in mechanical system simulations.

## Contribution

It establishes that the Lie-Trotter integrator is a Poisson integrator specifically for symmetric free rigid body dynamics, providing new insights into numerical methods for mechanical systems.

## Key findings

- Lie-Trotter integrator is a Poisson integrator for symmetric free rigid body
- Highlights importance of integrators in mechanical system analysis
- Provides theoretical foundation for numerical simulation accuracy

## Abstract

The numerical integration plays a fundamental role in understanding the behaviour of many mechanical systems. In this paper some important aspects of the mechanical integrators on the dynamics of a mechanical system are studied. More specific, we have shown that if that the Lie-Trotter integrator is obtained, in case of Euler equations for the dynamics of symmetric free rigid body, then it is a Poisson integrator. At the end of the paper some important remarks are presented.