2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/84167The use of generalized Lagrangians for describing elementary particles was already claimed by Ostrogradskii. It is shown how the spin structure of elementary particles arises if one allows the Lagrangian to depend on higher order derivatives. One part is related to the rotation of the particle and the other, which is coming from the dependence of the Lagrangian on the acceleration, is known as the zitterbewegung part of spin.Contribution to special issue in the 200th Ostrogradskii anniversary by the Journal of Ukrainian Mathematical SocietyClassical PhysicsGeneral Physicstext