{
  "id": "2212.11789",
  "version": "v1",
  "published": "2022-12-22T15:22:05.000Z",
  "updated": "2022-12-22T15:22:05.000Z",
  "title": "Euler's Equation via Lagrangian Dynamics with Generalized Coordinates",
  "authors": [
    "Dennis S. Bernstein",
    "Ankit Goel",
    "Omran Kouba"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is done by parameterizing the angular velocity vector in terms of 3-2-1 and 3-1-3 Euler angles as well as Euler parameters, that is, unit quaternions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-22T15:22:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lagrangian dynamics",
      "generalized coordinates",
      "eulers equation relates",
      "angular velocity vector",
      "euler parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}