Roman Matsyuk
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…
I proffer a development of some third order equation of motion for the free relativistic top from the simultaneously imposed assumptions of variationality and Lorentz symmetry.
A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimensional 'spin'-curvature interaction is investigated.
A family of Lagrange functions is considered, each producing the classical relativistic free spinning particle equation of motion of the third order. On this grounds a generalized Hamilton-Ostrohrads'kyj description of the free relativistic…
A variational equation of the fourth order for the free relativistic top is developed starting from the Dixon's system of equations for the motion of the relativistic dipole. The obtained equation is then cast into the homogeneous…
We prove that well known first-order (in spin, momentum, and space-time coordinates) equations of motion of relativistic top are equivalent to the third-order equations of Mathisson on the surface of the Mathisson-Pirani auxiliary…
We offer an example of the second order Kawaguchi metric function the extremal flow of which generalizes the flat space-time model of the semi-classical spinning particle to the framework of the pseudo-Riemannian space-time. The general…
The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.
The homogeneous canonical formalism of Rund is applied to the second-order Lagrangian model of the self-interacting particle of Bopp. The quasi-classical free spinning particle of Mathisson appears then as a constrained subsystem of the…
A second order variational description of the autoparallel curves of some differential-geometric connection for the third order Mathisson's 'new mechanics' of a relativistic free spinning particle is suggested starting from general…
Mathisson's 'new mechanics' of a relativistic spinning particle is shown to follow, in the case of planar motion, from only general requirements of relativistic invariance and of the dependence on third order derivatives along with the…