In this talk I will describe some objects of the generalized geometry that appear naturally in the qualitative analysis of mechanical systems. In particular we will discuss the Dirac structures within the framework of the systems with constraints and eventually of port-Hamiltonian systems. From the mathematical point of view, Dirac structures generalize simultaneously symplectic and Poisson structures. As for mechanics, the idea is to design numerical methods that preserve these structures and thus guarantee good physical behaviour in simulations. Then, I will present a framework which is even more general - the one of differential graded manifolds (also called Q-manifolds), and discuss some possible ways of using them for the "structure preserving integrators" in mechanics.

• [1] V. Salnikov, A. Hamdouni, From modelling of systems with constraints to generalized geometry and back to numerics, Z Angew Math Mech. 2019.
• [2] D. Razafindralandy, V. Salnikov, A. Hamdouni, A. Deeb, Some robust integrators for large time dynamics, AMSES, 2019.
• [3] V. Salnikov, A. Hamdouni, Geometric integrators in mechanics – the need for computer algebra tools, Proceedings of The third International Conference "Computer algebra", 2019, Moscow, Russia.
• [4] V. Salnikov, A. Hamdouni, Géométrie généralisée et graduée pour la mécanique, actes du Congrès Français de Mécanique, 2019, Brest, France.
• [5] V. Salnikov, A. Hamdouni, Differential Geometry and Mechanics - a source of problems for computer algebra, Programming and Computer Software, Vol. 46, Issue 2, 2020.