# Modeling three-dimensional surface-to-surface rigid contact and impact

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## Abstract

This work presents a rigid body framework for analyzing three-dimensional surface contacts and impacts as a simultaneous multi-point impact problem with friction. A method is developed to address the indeterminacy issue typically associated with multi-point contact and impact analysis. This is accomplished using the constraints on impulses and contact forces defined by the Coulomb friction law and rigid body constraints. The proposed approach relies on a global interpretation of Stronge’s energetic coefficient of restitution (ECOR) to maintain energetic consistency. A key aspect of this work involves addressing the three-dimensionality of this problem, which requires a numerical integration in the impulse domain to address the slip/no-slip behavior in the tangential plane of the impact. This work also models the transition to contact after a series of impacts, and proposes a method for enforcing frictional contact constraints. Several examples of simulation results using the proposed method are presented here.

## Keywords

Rigid body Impact Contact 3D model Coulomb friction Stronge hypothesis## Notes

## References

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