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We proceed from the fact that the classical paths of irreducible massivespinning particle lie on a circular cylinder with the time-like axis inMinkowski space. Assuming that all the classical paths on the cylinder aregauge-equivalent, we derive the equations of motion for the cylindrical curves.These equations are non-Lagrangian, but they admit interpretation in terms ofthe conditional extremum problem for a certain length functional in the classof paths subjected to the constant separation conditions. The unconditionalvariational principle is obtained after inclusion of constant separationconditions with the Lagrange multipliers into the action. We explicitly verifythat the states of the obtained model lie on the co-orbit of the Poincaregroup. The relationship with the previously known theory is demonstrated.

Variational principle for cylindrical curves and dynamics of spinning particles in $d=3$ Minkowski space