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.

翻译：本文提出了一种构建约束力学系统辛方法的新几何流程。通过引入源自回缩映射概念的定义映射，能够使连续问题适应离散化规则，而非相反。结果表明，约束子流形能够被辛离散流精确保持，且这些方法可扩展至非线性构型空间的情形。