{
  "abstract": "We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in inverse powers of the oscillation frequency $ω$. The explicit expression for the effective Lagrangian is derived up to ${\\cal O}(1/ω^6)$ next-to-next-to-leading approximation in the strong-drive regime. The general structure of the high-frequency expansion reveals a broad class of nonlinear systems whose transition curves are identical to those of the linear Mathieu equation, which enables a fully nonperturbative stability analysis in the case of strong driving and nonlinearity. The method is generalized to velocity-dependent forces and configuration space with curvature, characteristic to systems with constraints. Several applications are discussed in detail, including the dynamical magnetic trapping of electric charges.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.28996",
  "author_total": 2,
  "authors": [
    {
      "name": "Afshin Besharat"
    },
    {
      "name": "Alexander A. Penin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eg2f3s04ws4v5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.28996",
  "fulltext_url": null,
  "id": "eg2f3s04ws4v5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.28996",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "nlin.CD"
    ],
    [
      "arxiv",
      "physics.atom-ph"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.28996",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eg2f3s04ws4v5.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:14Z",
      "native_id": "2605.28996",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.28996"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.atom-ph",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Nonlinear Dynamics of Rapidly Driven Systems",
  "title_text": "Nonlinear Dynamics of Rapidly Driven Systems",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:49Z",
  "url": "https://research.draconitic.com/paper/eg2f3s04ws4v5",
  "venue": "arXiv",
  "versions": []
}