  We give a simple and self contained introduction to quaternions and their
practical usage in dynamics. The rigid body dynamics are presented in full
details. In the appendix, some more exotic relations are given that allow to
write more complex models, for instance, the one of a satellite with inertial
wheels and expressed in a non-inertial reference frame. As it is well known,
one nice advantage of quaternions over Euler angles, beside the usual
arguments, is that it allows to write down quite complex dynamics completely by
hand.
