{
  "id": "math/9910013",
  "version": "v1",
  "published": "1999-10-04T13:34:10.000Z",
  "updated": "1999-10-04T13:34:10.000Z",
  "title": "A numerical scheme for impact problems",
  "authors": [
    "Laetitia Paoli",
    "Michelle Schatzman"
  ],
  "comment": "47 pages; LaTeX plus Siam macros",
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider a mechanical system with impact and n degrees of freedom, written in generalized coordinates. The system is not necessarily Lagrangian. The representative point of the system must remain inside a set of constraints K; the boundary of K is three times differentiable. At impact, the tangential component of the impulsion is conserved, while its normal coordinate is reflected and multiplied by a given coefficient of restitution e between 0 and 1. The orthognality is taken with respect to the natural metric in the space of impulsions. We define a numerical scheme which enables us to approximate the solutions of the Cauchy problem: this is an ad hoc scheme which does not require a systematic search for the times of impact. We prove the convergence of this numerical scheme to a solution, which yields also an existence result. Without any a priori estimates, the convergence and the existence are local; with some a priori estimates, the convergence and the existence are proved on intervals depending exclusively on these estimates. This scheme has been implemented with a trivial and a non trivial mass matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-10-04T13:34:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65J10",
      "65M20",
      "65B05",
      "17B09",
      "46N20",
      "47D03"
    ],
    "keywords": [
      "numerical scheme",
      "impact problems",
      "non trivial mass matrix",
      "priori estimates",
      "convergence"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 522166,
      "adsabs": "1999math.....10013P"
    }
  }
}