{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:2d1c5e15-26a6-4ca8-816a-91461fc9e654",
  "labels": {
    "zh-CN": "最小作用量原理",
    "en": "principle of least action"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "599c4712c0975f36c6748596a2296fcca5cfdfbb83c8552e2d2a10e38ee2a666",
  "occurrences": [
    {
      "concept_id": "urn:uuid:2d1c5e15-26a6-4ca8-816a-91461fc9e654",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-35/01-lagrangian-mechanics",
      "anchor": "first-3d6fc0d9443abdc40360-zh",
      "chapter": "35",
      "section": "35.1",
      "offset": 1846,
      "range": [
        9442,
        9770
      ],
      "source_revision": "48e2b265db4401373b870b6f5b8ebf70c3e2bf2b83317cf43c97995540fe4a7c",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "最小作用量原理(principle of least action)",
      "context": {
        "range": [
          9378,
          9880
        ],
        "quote": "经典力学在拉格朗日形式下的基本原理是，经典轨迹由作用量泛函的临界点给出。这些临界点可能对应于作用量的极小值（因此这有时被称为“[<u class=\"concept-term\" data-concept-reference=\"concepts/mechanics/principle-of-stationary-action\" data-concept-identity=\"urn:uuid:2d1c5e15-26a6-4ca8-816a-91461fc9e654\" data-concept-route=\"/concept-identities#concept-2d1c5e15-26a6-4ca8-816a-91461fc9e654\" id=\"first-3d6fc0d9443abdc40360-zh\">最小作用量原理(principle of least action)</u>](../../../../../concepts/mechanics/principle-of-stationary-action)”），但对于不是作用量极小值的临界点，也能得到经典轨迹。可以如下定义临界点的适当概念：",
        "quote_sha256": "2ac4391e01e4db57232620b76abea206ec3e2bd1693e69f35b89a0c18e78c8d0",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-35/01-lagrangian-mechanics",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-d8fb1aab8a37ea7e2d850fea"
    },
    {
      "concept_id": "urn:uuid:2d1c5e15-26a6-4ca8-816a-91461fc9e654",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-35/01-lagrangian-mechanics",
      "anchor": "first-3d6fc0d9443abdc40360-en",
      "chapter": "35",
      "section": "35.1",
      "offset": 2361,
      "range": [
        9119,
        9438
      ],
      "source_revision": "3189a42e145bef0e89ec7c91298993eba1eee4ae7d40b3024fca2afa0c57535c",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "principle of least action",
      "context": {
        "range": [
          8876,
          9672
        ],
        "quote": "The fundamental principle of classical mechanics in the Lagrangian formalism is that classical trajectories are given by critical points of the action functional. These may correspond to minima of the action (so this is sometimes called the “[<u class=\"concept-term\" data-concept-reference=\"concepts/mechanics/principle-of-stationary-action\" data-concept-identity=\"urn:uuid:2d1c5e15-26a6-4ca8-816a-91461fc9e654\" data-concept-route=\"/concept-identities#concept-2d1c5e15-26a6-4ca8-816a-91461fc9e654\" id=\"first-3d6fc0d9443abdc40360-en\">principle of least action</u>](../../../../../concepts/mechanics/principle-of-stationary-action)”), but one gets classical trajectories also for critical points that are not minima of the action. One can define the appropriate notion of critical point as follows:",
        "quote_sha256": "9d46c420bd0630f58e226d7a8238267db1d34c5136c0ac1a253157263db51f86",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-35/01-lagrangian-mechanics",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-e8a0b46c92f8c2ce5b8edded"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-35/01-lagrangian-mechanics",
      "lang": "en",
      "section": "35.1",
      "signal": "term-mark",
      "label": "principle of least action",
      "english": "principle of least action",
      "offset": 1872
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-35/01-lagrangian-mechanics",
      "lang": "zh-CN",
      "section": "35.1",
      "signal": "term-mark",
      "label": "最小作用量原理",
      "english": "principle of least action",
      "offset": 1322
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-d8fb1aab8a37ea7e2d850fea",
    "occ-e8a0b46c92f8c2ce5b8edded"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "5f2bac12e5954933c9a3acf89f28660470b3ab1484be11e0d3fc948cf69b3f41",
  "optional_enrichments": []
}
