Abstract

In this paper we give an overview of results relating the recent “discoveries” in differential geometry, such as higher structures and differential graded manifolds, with some natural problems coming from mechanics. We explain that a lot of classical differential geometric constructions in this context can be conveniently described using the language of $Q$-structures, and thus $Q$-structure preserving integrators are potentially of great use in mechanics. We give some hints how the latter can be constructed and formulate some open problems.

Since this paper is intended for both the mathematics and mechanics communities, we tried to make it accessible to nongeometers as well.

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