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arXiv · 2306.06786

A new perspective on symplectic integration of constrained mechanical systems via discretization maps

María Barbero Liñán·David Martín de Diego·Rodrigo T. Sato Martín de Almagro
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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.

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María Barbero Liñán, David Martín de Diego, Rodrigo T. Sato Martín de Almagro. 2023-06-11. A new perspective on symplectic integration of constrained mechanical systems via discretization maps. https://arxiv.org/abs/2306.06786

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