8 citations · 35 across the 20 of their papers we have counts for
21 papers
Relativistic mechanics of constant curvature
R. Ya. Matsyuk
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physical…
Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics
Roman Ya. Matsyuk
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach whic…
Third order variational equation for the free relativistic top
Roman Matsyuk
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.
Differential geometric mechanisms in Ostrohrads'kyj relativistic spherical top dynamics
R. Ya. Matsyuk
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of…
Variationality with second derivatives, relativistic uniform acceleration, and the 'spin'-curvature interaction in two-dimensional space-time
Roman Matsyuk
A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimen…
Quasi-Hamiltonian description of classical spin
Roman Matsyuk
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…