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A new perspective on symplectic integration of constrained mechanical systems via discretization maps (2306.06786v2)
Published 11 Jun 2023 in math.NA, cs.NA, math-ph, and math.MP
Abstract: A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the discretization rule rather than viceversa. As a result, the constraint submanifold is exactly preserved by the symplectic discrete flow and the extension of these methods to the case of non-linear configuration spaces is doable.