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| Dirac structures were introduced by A. Weinstein and T.J. Courant in 1987 as a geometric structure unifying Poisson and presymplectic structures, with a motivation from the Dirac theory of constraints. Since then, Dirac geometry has evolved in several directions. Part of its versatility, as compared with Poisson or symplectic geometry, comes from the transformation properties of Dirac structures, which leads to a unification of several fundamental physical models. This includes Lagrangian and Hamiltonian mechanics, nonholonomic mechanics, control, optimal control and interconnected systems. I will expose some recent developments in this direction. |
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