We present two meaningful and effective non-ideal constitutive characterizations for a multiple impulsive constraints \({\mathcal {S}}\) comprising a finite number of non-ideal frictionless constraints of codimension 1, described in the geometric setup given by the space–time bundle \({\mathcal {M}}\) of a mechanical system in contact/impact with \({\mathcal {S}}\). Thanks to the geometric structures associated to the elements of \({\mathcal {S}}\), we introduce a symmetric characterization, that does not distinguish the elements forming \({\mathcal {S}}\) as regards mechanical behavior, and an asymmetric one that makes this distinction. Both the characterizations provide a generalization of the characterization of ideal multiple constraints presented in Pasquero (Q Appl Math 76(3):547–576, 2018). The iterative nature of these characterizations allows the introduction of two algorithms determining the right velocity of the system in case of single or multiple contact/impact with symmetric or asymmetric constraints \({\mathcal {S}}\), once the elements forming \({\mathcal {S}}\) and the left velocity of the system are known. We show the effectiveness of the two possible choices with explicit implementations of these algorithms in two significant examples: a simplified Newton’s cradle system for the symmetric characterization and a disk in multiple contact/impact with two walls of a corner for the asymmetric one.

我们针对多重脉冲约束\（{\ mathcal {S}} \）提出了两个有意义且有效的非理想本构刻画，其中包括有限数量的余维1的非理想无摩擦约束，在空间给出的几何设置中进行了描述–与/ （{\ mathcal {S}} \\）接触/碰撞的机械系统的时间束\（{\ mathcal {M}} \ }。由于与\（{\ mathcal {S}} \}的元素相关联的几何结构，我们引入了对称特征，它不能区分形成\（{\ mathcal {S}} \）的元素关于机械性能，以及一种不对称的特性。两种表征都对Pasquero中提出的理想多重约束的表征进行了概括（Q Appl Math 76（3）：547-576，2018）。这些特征的迭代性质允许引入两种算法，以在具有对称或不对称约束\（{\ mathcal {S}} \}的单接触或多接触/碰撞的情况下确定系统的正确速度，一旦元素形成\ （{\数学{S}} \）和系统的左速度是已知的。我们在两个重要的示例中展示了这些算法的显式实现的两种可能选择的有效性：用于对称特征的简化牛顿摇篮系统，以及用于非对称角的两角壁的多次接触/碰撞的磁盘。