Symmetric and Asymmetric Multiple Impulsive Constraints Without Friction and Their Characterization

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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.