A generalised relativistic Lagrangian is suggested, which is such that the momentum vector possesses a component normal to the direction of the velocity, while the conservation of total angular momentum requires the existence of a non-vanishing internal angular momentum tensor (spin). The resulting mechanical system is very similar to the spin models of elementary particles discussed by Hönl, Papapetrou, Bopp and others, as these emerge as special cases. Although the latter are usually derived from variational principles for which the Lagrangian depends on the acceleration, the present theory is based on a Lagrangian depending solely on position and velocity. This method avoids certain mathematical difficulties, and permits the immediate application of the Hamiltonian theory associated with such simple variational principles. Although no radiation effects are considered, the Abraham vector plays an important role in this purely mechanical theory.