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Geometric Mechanics and Control Theory

Geometric mechanics involves the study of Lagrangian, Hamiltonian mechanics and control theory using geometric and symmetry techniques. The main guiding idea in its development consists in applying the techniques and methods of differential geometry to the study and description of this kind of systems (classical, field theoretical, or quantum). It can be applied to design new structured algorithms for the numerical study of these systems that capture their essential qualitative behaviours and improve the stability properties of the existing methods.