Resumen de Co-Adjoint representation and controllability

Víctor Ayala, Luis B. Vergara

• Let Σ an invariant control system over Lie group G The existence of a nontrivial simplectic orbit of G is analysed, so that the Hamiltonian system equivalent to Σ via the co-adjoint representation, has a vector called simplectic. This allows the construction of a strictly increasing function over the positive trajectories of Σ, determining sufficient conditions for the controllability of Σ over G.