Classification of rotational motions for the baryon model “triangle”

A baryon model with three particles (quarks) pairwise connected by relativistic strings forming a curvilinear triangle is considered. The classical analytic solutions corresponding to a uniform plane rotation of the system with arbitrary quark masses $m_i$ are found for this model. The sections of the related world surfaces by the plane $t=\mathrm{const}$ are curvilinear triangles composed of segments of a hypocycloid. A complete classification of the types of motion is suggested, based on differences in topological configuration and the presence and number of interior massless points on the string that move at the velocity of light. The classification results from investigating the limiting states as $m_i\to 0$. The calculated energy dependence of the angular momentum of the motions creates possibilities to model baryon states on Regge trajectories using these motions.