{
  "annotation_id": "be5d8420-7ce3-438b-a2cd-98a7007972bd",
  "date_created": "2026-03-02T18:01:45.462000Z",
  "date_modified": "2026-03-02T18:01:45.462000Z",
  "file_hash": "ce46234ff409af5825fafecd651f7835ed08d374123675a4719defd17cfa0f8d",
  "private": false,
  "record": {
    "abstract": "Given two linearly independent matrices in $so(3)$, $Z_1$ and $Z_2$, every\nrotation matrix $X_f \\in SO(3)$ can be written as the product of alternate\nelements from the one dimensional subgroups corresponding to $Z_1$ and $Z_2$,\nnamely $X_f=e^{Z_1 t_1}e^{Z_2 t_2}e^{Z_1t_3} \\cdot \\cdot \\cdot e^{Z_1t_s}$. The\nparameters $t_i$, $i=1,...,s$ are called {\\it generalized Euler angles}.\n  In this paper, we evaluate the minimum number of factors required for the\nfactorization of $X_f \\in SO(3)$, as a function of $X_f$, and provide an\nalgorithm to determine the generalized Euler angles explicitly. The results can\nbe applied to the bang bang control with minimum number of switches of some\nclassical control systems and of two level quantum systems.",
    "arxiv_id": "quant-ph/0110120",
    "authors": [
      "Domenico D\u0027Alessandro"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Optimal Evaluation of Generalized Euler Angles with Applications to   Classical and Quantum Control",
    "url": "https://arxiv.org/abs/quant-ph/0110120"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "116b3581-6e9c-4045-858f-bf18c38a7a11",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}