{
  "abstract": "We construct finite-dimensional Lie-group summaries of based rotational paths that retain the exact terminal attitude and selected iterated angular-velocity integrals. These summaries, called rotational trajectory synopses, compose exactly under path concatenation. Building on the classical works of Magnus and Chen, we establish endpoint-retaining body, spatial, and hybrid synopsis groups at every finite order and give a uniform matrix realization for the evaluated Magnus hierarchy. We distinguish this hierarchy from the full Chen signature from order three onward and prove \\chg{that the exact endpoint is independent of every finite truncation of the body, spatial, or combined angular-velocity signature: the synopsis maps are surjective at every finite order}. An underactuated satellite example connects the retained coordinates to geometric phase in spacecraft attitude dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01691",
  "author_total": 2,
  "authors": [
    {
      "name": "Gregory S. Chirikjian"
    },
    {
      "name": "Taeyoung Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/056njn9zzja60.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01691",
  "fulltext_url": null,
  "id": "056njn9zzja60",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01691",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2207|Control and Stability of Dynamical Systems"
    ]
  ],
  "openalex": "W7216415338",
  "pdf_url": "https://arxiv.org/pdf/2610.01691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/056njn9zzja60.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Rotational Trajectory Synopsis Groups",
  "title_text": "Rotational Trajectory Synopsis Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/056njn9zzja60",
  "venue": "arXiv",
  "versions": []
}