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Abstract
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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
-structures, and
thus
-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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Keywords
Dirac structures, differential graded manifolds,
theoretical mechanics, geometric integrators
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Mathematical Subject Classification
Primary: 70G45, 58A50, 70H45, 70H30
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Milestones
Received: 16 July 2020
Revised: 14 September 2020
Accepted: 29 October 2020
Published: 17 March 2021
Communicated by Francesco dell'Isola
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