General solution to the Euler-Poisson equations of a free Lagrange top directly for the rotation matrix

TL;DR

This paper presents a general analytic solution to the Euler-Poisson equations for a free Lagrange top, avoiding traditional parameterizations, and compares it with classical Poinsot's motion visualization.

Contribution

It provides a novel, direct solution for the rotation matrix of a free Lagrange top without relying on Euler angles or other parameterizations.

Findings

Derived a general analytic solution to the Euler-Poisson equations

Compared the solution with Poinsot's geometric interpretation

Enhanced understanding of free Lagrange top dynamics

Abstract

The Euler-Poisson equations para determinar the rotation matrix of a rigid body can be solved without using of particular parameterization like the Euler angles. For the free Lagrange top, we obtain and discuss a general analytic solution, and compare it with the Poinsot's picture of motion.