Skip to main content
SpringerLink
Log in

Collision of three balls on a plane

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

We consider three rigid balls moving on a plane and investigate their multiple collisions (i.e., the three balls collide at the same time). This is a 3D problem because balls may jump. We develop a predictive theory based on the idea that the system made of three balls and a plane is deformable. As shown by the examples, the theory accounts for the physical properties of multiple collisions and its main feature is the presence of non local interactions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Brogliato B (1999) Non-smooth mechanics, 2nd edn. Springer, Berlin

    Google Scholar 

  2. Dimnet E (2002) Mouvement et collisions de solides rigides et déformables. PhD Thesis. Ecole nationale des Ponts et Chaussées, Paris

  3. Frémond M (2000) Collision of a wedge with a plane. J Comput Appl Math 19(2): 127–136

    MATH  Google Scholar 

  4. Frémond M (2002) Non-smooth thermomechanics. Springer, Heidelberg

    MATH  Google Scholar 

  5. Frémond M (2007) Collisions. Department of Civil Engineering, University of Rome “Tor Vergata”, Rome

  6. Halphen B, Nguyen QS (1975) Sur les matériaux standard généralisés. J Mécanique 14: 39–63

    MATH  Google Scholar 

  7. Jean M, Moreau JJ (1992) Unilaterality and dry friction in the dynamics of rigid body collections. In: Curnier A (ed) Proceedings of contact mechanics international symposium. Presses Polytechniques et Universitaires Romandes, Lausanne, pp 31–48

  8. Minty GJ (1962) Monotone (non linear) operators in Banach spaces. Duke Math J 29: 341–346

    MATH  MathSciNet  Google Scholar 

  9. Moreau JJ (1970) Sur les lois de frottement, de viscosité et de plasticité. C R Acad Sci Sér A 271: 608–611

    Google Scholar 

  10. Moreau JJ (2003) Fonctionnelles convexes. Department of Civil Engineering, University of Rome “Tor Vergata”, Rome and (1966) Séminaire sur les équations aux dérivées partielles, Collège de France, Paris

  11. Nayroles B (1974) Point de vue algébrique, convexité et intégrandes convexes en mécanique des solides. In: New variational techniques in mathematical physics. Ed. Cremonese, Rome, pp 325–404

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of Roma “Tor Vergata”, 00133, Rome, Italy

    Federica Caselli & Michel Frémond

Authors
  1. Federica Caselli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michel Frémond
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Federica Caselli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Caselli, F., Frémond, M. Collision of three balls on a plane. Comput Mech 43, 743–754 (2009). https://doi.org/10.1007/s00466-008-0342-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-008-0342-7

Keywords

Search

Navigation