ON SOME GEOMETRIC ASPECTS OF EVOLUTION VARIATIONAL PROBLEMS

The main objective of the work is to identify the relationship between evolution equations with potential operators and geometries of related configuration spaces of the given systems. Using the Hamilton principle, a wide class of such equations is derived. Their structural analysis is carried out, containing operator analogues of the Christoffel symbols of both the 1st and 2nd kind. It is shown that the study of the obtained evolution equations can be associated, in general, with an extended configuration space, the metric of which is determined by the kinetic energy of the given system.