8 citations · 35 across the 20 of their papers we have counts for
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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.
Second order variational problem and 2-dimensional concircular geometry
Roman Matsyuk
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…
A first order prolongation of the conventional space
R. Ya. Matsyuk
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
Symmetries of vector exterior differential systems and the inverse problem in second-order Ostrohrads'kyj mechanics
R. Ya. Matsyuk
Symmetries of variational problems are considered as symmetries of vector bundle valued exterior differential systems. This approach is then applied to third order ordinary variati…
Integration by parts and vector differential forms in higher order variational calculus on fibred manifolds
Roman Ya. Matsyuk
Infinitesimal variation of Action functional in classical (non-quantum) field theory with higher derivatives is presented in terms of well-defined intrinsic geometric objects indep…