A new 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 discrete flow and the extension of the methods to the case of non-linear configuration spaces is straightforward.

翻译：本文提出了一种构造约束力学系统辛积分方法的新流程。通过引入由收缩映射概念导出的映射定义，使得连续问题能够适应离散化规则，而非传统意义上的反向适配。该方法的离散流可精确保持约束子流形，且能直接推广至非线性构型空间场景。