Analytical solution of the Euler-Poinsot problem

Abstract

In the present paper, an analysis was performed on the torque-free motion of a rigid body, developing Euler's analytical solution and Poinsot's geometric solution. From mathematical formulations, the analytical solution for the time evolution of the angular velocity and Euler's angles was obtained and described given some initial conditions. Besides, an animation of Poinsot's geometric solution was elaborated and a study was carried out on the conditions in which the herpolhode forms a closed curve. Finally, an algorithm was developed in the software Scilab that displays the analytical and numerical solutions obtained, it also generates an animation of the geometric solution, moreover to having an algorithm that generates closed herpolhodes.