Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

In the community of people working in Geometric Mechanics it is well-known that (Lie) algebroids provide an elegant language to describe Lagrangian mechanics and variational calculus. However, it is not that clear what geometric structures should we use to describe theories involving derivatives of order higher than one. In the talk we will propose a class of such structures - higher analogs of algebroids. Our theory is based on two elegant geometric concepts: a graded bundle and a Zakrzewski morphism (a differential relation of a special kind) .