{
  "annotation_id": "55c750d4-1c8f-4c47-9eb2-7c2f79346a35",
  "date_created": "2026-03-02T18:01:00.638000Z",
  "date_modified": "2026-03-02T18:01:00.638000Z",
  "file_hash": "0ba3bb29cb5856968e424331d09b24a7b030ec8db2bd5d57634ebefcf456e27b",
  "private": false,
  "record": {
    "abstract": "We reexamine a very classical problem, the spinning behavior of the tippe top\non a horizontal table. The analysis is made for an eccentric sphere version of\nthe tippe top, assuming a modified Coulomb law for the sliding friction, which\nis a continuous function of the slip velocity $\\vec v_P$ at the point of\ncontact and vanishes at $\\vec v_P=0$. We study the relevance of the gyroscopic\nbalance condition (GBC), which was discovered to hold for a rapidly spinning\nhard-boiled egg by Moffatt and Shimomura, to the inversion phenomenon of the\ntippe top. We introduce a variable $\\xi$ so that $\\xi=0$ corresponds to the GBC\nand analyze the behavior of $\\xi$. Contrary to the case of the spinning egg,\nthe GBC for the tippe top is not fulfilled initially. But we find from\nsimulation that for those tippe tops which will turn over, the GBC will soon be\nsatisfied approximately. It is shown that the GBC and the geometry lead to the\nclassification of tippe tops into three groups: The tippe tops of Group I never\nflip over however large a spin they are given. Those of Group II show a\ncomplete inversion and the tippe tops of Group III tend to turn over up to a\ncertain inclination angle $\\theta_f$ such that $\\theta_f\u003c\\pi$, when they are\nspun sufficiently rapidly. There exist three steady states for the spinning\nmotion of the tippe top. Giving a new criterion for stability, we examine the\nstability of these states in terms of the initial spin velocity $n_0$. And we\nobtain a critical value $n_c$ of the initial spin which is required for the\ntippe top of Group II to flip over up to the completely inverted position.",
    "arxiv_id": "physics/0507198",
    "authors": [
      "Takahiro Ueda",
      "Ken Sasaki",
      "Shinsuke Watanabe"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "doi": "10.1137/040615985",
    "journal_ref": "SIAM J. Applied Dynamical Systems Vol. 4 pp. 1159-1194 (2005)",
    "title": "Motion of the Tippe Top : Gyroscopic Balance Condition and Stability",
    "url": "https://arxiv.org/abs/physics/0507198"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0d28d0f7-ba58-43ab-a137-02ee426108dd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}