  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 any 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.
