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In this note we describe how some objects from generalized geometry appear inthe qualitative analysis and numerical simulation of mechanical systems. Inparticular we discuss double vector bundles and Dirac structures. It turns outthat those objects can be naturally associated to systems with constraints --we recall the mathematical construction in the context of so called implicitLagrangian systems. We explain how they can be used to produce new numericalmethods, that we call Dirac integrators.  On a test example of a simple pendulum in a gravity field we compare theDirac integrators with classical explicit and implicit methods, we pay specialattention to conservation of constrains. Then, on a more advanced example ofthe Ziegler column we show that the choice of numerical methods can indeedaffect the conclusions of qualitative analysis of the dynamics of mechanicalsystems. We also tell why we think that Dirac integrators are appropriate forthis kind of systems by explaining the relation with the notions of geometricdegree of non-conservativity and kinematic structural stability.

From modelling of systems with constraints to generalized geometry and back to numerics