相关论文: A covering second-order Lagrangian for the relativ…

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 analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…

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 free relativistic top in three-dimensional space-time. The…

The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…

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…

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) for each second-order Lagrangian density on an arbitrary fibred manifold $p\colon E\to N$ the Poincar\'e-Cartan form of which is…

We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with multi-valued dependent functions of several variables. Our…

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 which consists in the simultaneous imposition of symmetry…

Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic…

Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, how-ever, of sheaf-theoretic…

Symmetries in the Lagrangian formalism of arbitrary order are analysed with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second order equations and a scalar field we establish a polynomial structure in the…

We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second…

A second-order generalization of the fundamental Lepage form of geometric calculus of variations over fibered manifolds with 2-dimensional base is described by means of insisting on (i) equivalence relation "Lepage differential 2-form is…

We describe a new BF-type first-order in derivatives Lagrangian for General Relativity. The Lagrangian depends on a connection field as well as a Lie-algebra valued two-form field, with no other fields present. There are two free…

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.

We obtain regularity conditions of a new type of problems of the calculus of variations with second-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main result asserts that autonomous integral…

We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh…

We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The integral functional is extended to the space of measures. The obtained second-order derivatives contain integrals on…

We address the problem of the existence of a Lagrangian for a given system of linear PDEs with constant coefficients. As a subtask, this involves bringing the system into a pre-Lagrangian form, wherein the number of equations matches the…

Relativistic systems of particles interacting pairwise at a distance (interactions not mediated by fields) in flat spacetime are studied. It is assumed that the interactions propagate at the speed of light in vacuum and that all masses are…