The angular velocity of a rigid body is usually described in classical mechanics courses by using Euler angles. However, in order to avoid singularity problems on the numerical integration of the motion equations, another ways are more interesting. Among them, the quaternions are a very popular choice and with a strong practical appeal on the parameterization and integration of the Euler's equations. In this sense, this paper proposes a comparison between the numerical integration of the Euler equations of a gyroscope with the inverse kinematics solved through Euler angles and by quaternions, that are not commonly described in classical mechanics textbooks on a first mechanical course. The goal is to show that apart the numerical asset, the integration of the motion equations with the quaternions parameterization also can be used with a noblest didactical way: to introduce and motivate the students with the use of others more advanced algebraic systems, as Geometric Algebra (Clifford's Algebra).
Keywords:
Gyroscope; Quaternions; Euler Angles; Geometric Algebra; Rigid Body Rotation in Space
