8 citations · 35 across the 20 of their papers we have counts for
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Variational generalization of free relativistic top
Roman Matsyuk
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 Mathisso…
Towards the physical significance of the metric
Roman Matsyuk
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 fr…
Variationality of geodesic circles in two dimensions
R. Ya. Matsyuk
This note treats the notion of Lagrange derivative for the third order mechanics in the context of covariant Riemannian geometry. The variational differential equation for geodesic…
The next variational prolongation of the Euclidean space
Roman Matsyuk
The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.
Canonical formalism for quasi-classical particle "Zitterbewegung" in Ostrohrads'kyj mechanics
Roman Matsyuk
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…
Autoparallel variational description of the free relativistic top third order dynamics
Roman Matsyuk
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 s…