The present paper deals with the geometry of the tangent bundle over a differentiable (Cr)
manifold, and with the so-called inverse problem of Lagrangian dynamics. There are various …

Even though in classical mechanics the dynamical evolution of a system is completely
characterized by Newton's equations, the idea of formulating the theory in terms of a …

This work starts with classical equations of motion and sets very general quantization
conditions (commutation relations). It is proved that these conditions imply that the equations …

One presents numerous approaches for the construction of variational principles for
equations with operators which, in general, are nonpotential. One considers separately …

A new kind of Lagrangian symmetry is defined in such a way that the resulting set of
Lagrangian symmetries coincides with the set of symmetries of its equations of motion …

We study the constrained Ostrogradski-Hamilton framework for the equations of motion
provided by mechanical systems described by second-order derivative actions with a linear …

Recently obtained results linking several constants of motion to one (non-Noetherian)
symmetry to the problem of geodesic motion in Riemannian space-times are applied. The …

The problem of the correspondence between symmetries and conservation laws for partial
differential equations is considered. For Lagrangian systems the set of Noether (variational) …

A set X Gamma of vector fields in the evolution space E playing the role of Newtonian vector
fields, with respect to a second-order equation field Gamma, is introduced and endowed …

The Helmholtz conditions are the necessary and sufficient conditions for a set of second-
order differential equations to be equivalent to a variational principle. In this work an …