{
  "aliases": [
    "constant-of-motion",
    "conserved-quantity"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "0SS1P1YC9A"
    }
  ],
  "body": "\n## Summary\n\nA first integral, or constant of motion, of a system of differential equations is a function of the state that stays constant along each solution.\nEnergy, linear momentum and angular momentum are common examples in mechanics. See the [[definition|0SS1P1YC9A]].\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "aliases": [
      "constant-of-motion",
      "conserved-quantity"
    ],
    "kind": "concept",
    "msc": [
      "34C14"
    ],
    "name": "First integral",
    "same_as": {
      "wikidata": "Q647631",
      "wikipedia": "Constant of motion"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Constant_of_motion"
      }
    ],
    "tag": "0262JP0NV9"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0262JP0NV9/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0262JP0NV9.md",
  "msc": [
    "34C14"
  ],
  "name": "First integral",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/026/0262JP0NV9.md",
  "status": null,
  "tag": "0262JP0NV9",
  "uri": "m2://0262JP0NV9",
  "url": "https://math2.tamnd.com/wiki/first-integral/",
  "writing": {
    "tag": "0262JP0NV9",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}