In this paper, consideration is given to a baryon model in which three
material points (quarks) are pairwise connected by relativistic strin
gs forming a curvilinear triangle. For this model, we found and studie
d classical solutions corresponding to a uniform rotation of the syste
m in a plane about the center of mass. Along with the simplest state-a
rotating curvilinear triangle with smooth sides-there can be more com
plicated configurations characterized by the motion, at the velocity o
f light, of some interior massless points of the string. In the limit,
the closed string takes the form of a rotating hypocycloid as the qua
rk masses tend to zero. The possibility of describing baryon states on
Regge trajectories with the help of the above-mentioned solutions is
analyzed.