  This paper studies various aspects of the motion of relativistic rotators,
both in the presence and absence of external fields, using a toy model which,
in a sense, can be regarded as a non-relativistic limit of the rotators. In a
simpler setup, this enables one to gain an insight into the principal
difference between mechanical systems with singular and non-singular Hessian,
whilst avoiding the complications resulting from the more intricate form of the
equations of motion in the fully relativistic regime. In particular, one can
comprehend the apparent contradiction between Hessian singularity and
simultaneous occurrence of unique solutions for the motion of the fundamental
relativistic rotator minimally coupled to the electromagnetic field. With the
aid of the toy model the author supports and illustrates his thesis put forward
elsewhere that the Hessian singularity is a defect that makes physically
unviable some geometric models of spinning particles considered in the
literature.
