Solução geral das equações de Euler - Poisson de um corpo com simetria axial

Abstract

Euler-Poisson equations describe the temporal evolution of a rigid body’s orientation through the rotation matrix and angular velocity components, governed by first-order differential equations. According to the Cauchy-Kovalevskaya theorem, these equations can be solved by expressing their solutions as power series in the evolution parameter. In this work, we obtain the general solution to this system in elementary functions by direct computation, deriving the sum of these series for the case of a free symmetric rigid body, without using euler angles. This results are recently published in an international journal: Guilherme Corrêa Silva, General solution to Euler - Poisson equations of a free symmetric rigid body by direct summation of power series, Archive of Applied Mechanics (2025) 96:68, https://doi.org/10.1007/s00419-025-02774-y. The results are consistent with previous studies, offering a new perspective (the last one in emphasis) on solving the Euler-Poisson equations. In addition, we provide a thorough analysis of the dynamics of a rigid body, treating it as a system subject to kinematic constraints. We derive all the fundamental quantities and properties of a rigid body, along with its equations of motion and conserved quantities, through direct and clear calculations from the variational problem, using the established techniques of classical mechanics.