mathmlben/data/86.json

Visualization for goldstandard

{
  "definitions" : {
    "L" : [ "Lagrange function", {
      "Q505735" : "Lagrangian"
    } ],
    "q_{i}" : [ {
      "Q1057607" : "Generalized coordinates"
    } ],
    "t" : [ {
      "Q11471" : "time (dimension in which events can be ordered from the past through the present into the future)"
    } ],
    "\\dot{q_{i}}" : [ "generalized velocities", {
      "Q1057607" : "Generalized coordinates"
    } ]
  },
  "constraints" : [ ],
  "math_inputtex" : "\n{\\partial{L}\\over \\partial q_i} = {\\mathrm{d} \\over \\mathrm{d}t}{\\partial{L}\\over \\partial{\\dot{q_i}}}.\n",
  "math_inputtex_semantic" : "{\\partial{\\wf{Q505735}{L}}\\over \\partial \\w{Q505735}{q}_i} = {\\mathrm{d} \\over \\mathrm{d}t}{\\partial{L}\\over \\partial{\\dot{q_i}}}",
  "correct_tex" : "{\\partial{L}\\over \\partial q_i} = {\\mathrm{d} \\over \\mathrm{d}t}{\\partial{L}\\over \\partial{\\dot{q_i}}}",
  "correct_mml" : "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"p1.1.m1.1\" class=\"ltx_Math\" alttext=\"{\\partial{L}\\over\\partial q_{i}}={\\mathrm{d}\\over\\mathrm{d}t}{\\partial{L}\\over%&#10;\\partial{\\dot{q_{i}}}}\" display=\"inline\">\n  <semantics id=\"p1.1.m1.1a\">\n    <mrow id=\"p1.1.m1.1.5\" xref=\"p1.1.m1.1.5.cmml\">\n      <mfrac id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">\n        <mrow id=\"p1.1.m1.1.1.2\" xref=\"p1.1.m1.1.1.2.cmml\">\n          <mo id=\"p1.1.m1.1.1.2.1\" xref=\"p1.1.m1.1.1.2.1.cmml\">∂</mo>\n          <mo id=\"p1.1.m1.1.1.2a\" xref=\"p1.1.m1.1.1.2.cmml\">⁡</mo>\n          <mi id=\"p1.1.m1.1.1.2.2\" xref=\"p1.1.m1.1.1.2.2.cmml\">L</mi>\n        </mrow>\n        <mrow id=\"p1.1.m1.1.1.3\" xref=\"p1.1.m1.1.1.3.cmml\">\n          <mo id=\"p1.1.m1.1.1.3.1\" xref=\"p1.1.m1.1.1.3.1.cmml\">∂</mo>\n          <mo id=\"p1.1.m1.1.1.3a\" xref=\"p1.1.m1.1.1.3.cmml\">⁡</mo>\n          <msub id=\"p1.1.m1.1.1.3.4\" xref=\"p1.1.m1.1.1.3.4.cmml\">\n            <mi id=\"p1.1.m1.1.1.3.2\" xref=\"p1.1.m1.1.1.3.2.cmml\">q</mi>\n            <mi id=\"p1.1.m1.1.1.3.3.1\" xref=\"p1.1.m1.1.1.3.3.1.cmml\">i</mi>\n          </msub>\n        </mrow>\n      </mfrac>\n      <mo id=\"p1.1.m1.1.2\" xref=\"p1.1.m1.1.2.cmml\">=</mo>\n      <mrow id=\"p1.1.m1.1.5.1\" xref=\"p1.1.m1.1.5.1.cmml\">\n        <mfrac id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">\n          <mi mathvariant=\"normal\" id=\"p1.1.m1.1.3.2\" xref=\"p1.1.m1.1.3.2.cmml\">d</mi>\n          <mrow id=\"p1.1.m1.1.3.3\" xref=\"p1.1.m1.1.3.3.cmml\">\n            <mi mathvariant=\"normal\" id=\"p1.1.m1.1.3.3.1\" xref=\"p1.1.m1.1.3.3.1.cmml\">d</mi>\n            <mo id=\"p1.1.m1.1.3.3.3\" xref=\"p1.1.m1.1.3.3.3.cmml\">⁢</mo>\n            <mi id=\"p1.1.m1.1.3.3.2\" xref=\"p1.1.m1.1.3.3.2.cmml\">t</mi>\n          </mrow>\n        </mfrac>\n        <mo id=\"p1.1.m1.1.5.1.1\" xref=\"p1.1.m1.1.5.1.1.cmml\">⁢</mo>\n        <mfrac id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.4.cmml\">\n          <mrow id=\"p1.1.m1.1.4.2\" xref=\"p1.1.m1.1.4.2.cmml\">\n            <mo id=\"p1.1.m1.1.4.2.1\" xref=\"p1.1.m1.1.4.2.1.cmml\">∂</mo>\n            <mo id=\"p1.1.m1.1.4.2a\" xref=\"p1.1.m1.1.4.2.cmml\">⁡</mo>\n            <mi id=\"p1.1.m1.1.4.2.2\" xref=\"p1.1.m1.1.4.2.2.cmml\">L</mi>\n          </mrow>\n          <mrow id=\"p1.1.m1.1.4.3\" xref=\"p1.1.m1.1.4.3.cmml\">\n            <mo id=\"p1.1.m1.1.4.3.1\" xref=\"p1.1.m1.1.4.3.1.cmml\">∂</mo>\n            <mo id=\"p1.1.m1.1.4.3a\" xref=\"p1.1.m1.1.4.3.cmml\">⁡</mo>\n            <mover accent=\"true\" id=\"p1.1.m1.1.4.3.2\" xref=\"p1.1.m1.1.4.3.2.cmml\">\n              <msub id=\"p1.1.m1.1.4.3.2.2\" xref=\"p1.1.m1.1.4.3.2.2.cmml\">\n                <mi id=\"p1.1.m1.1.4.3.2.2.1\" xref=\"p1.1.m1.1.4.3.2.2.1.cmml\">q</mi>\n                <mi id=\"p1.1.m1.1.4.3.2.2.2.1\" xref=\"p1.1.m1.1.4.3.2.2.2.1.cmml\">i</mi>\n              </msub>\n              <mo id=\"p1.1.m1.1.4.3.2.1\" xref=\"p1.1.m1.1.4.3.2.1.cmml\">˙</mo>\n            </mover>\n          </mrow>\n        </mfrac>\n      </mrow>\n    </mrow>\n    <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n      <apply id=\"p1.1.m1.1.5.cmml\" xref=\"p1.1.m1.1.5\">\n        <eq id=\"p1.1.m1.1.2.cmml\" xref=\"p1.1.m1.1.2\"/>\n        <apply id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">\n          <divide id=\"p1.1.m1.1.1.1.cmml\" xref=\"p1.1.m1.1.1\"/>\n          <apply id=\"p1.1.m1.1.1.2.cmml\" xref=\"p1.1.m1.1.1.2\">\n            <partialdiff id=\"p1.1.m1.1.1.2.1.cmml\" xref=\"p1.1.m1.1.1.2.1\"/>\n            <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.2.2.cmml\" xref=\"p1.1.m1.1.1.2.2\">Q505735</csymbol>\n          </apply>\n          <apply id=\"p1.1.m1.1.1.3.cmml\" xref=\"p1.1.m1.1.1.3\">\n            <partialdiff id=\"p1.1.m1.1.1.3.1.cmml\" xref=\"p1.1.m1.1.1.3.1\"/>\n            <apply id=\"p1.1.m1.1.1.3.4.cmml\" xref=\"p1.1.m1.1.1.3.4\">\n              <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.1.3.4.1.cmml\" xref=\"p1.1.m1.1.1.3.4\">subscript</csymbol>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.1.3.2.cmml\" xref=\"p1.1.m1.1.1.3.2\">Q505735</csymbol>\n              <ci id=\"p1.1.m1.1.1.3.3.1.cmml\" xref=\"p1.1.m1.1.1.3.3.1\">𝑖</ci>\n            </apply>\n          </apply>\n        </apply>\n        <apply id=\"p1.1.m1.1.5.1.cmml\" xref=\"p1.1.m1.1.5.1\">\n          <times id=\"p1.1.m1.1.5.1.1.cmml\" xref=\"p1.1.m1.1.5.1.1\"/>\n          <apply id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\">\n            <divide id=\"p1.1.m1.1.3.1.cmml\" xref=\"p1.1.m1.1.3\"/>\n            <ci id=\"p1.1.m1.1.3.2.cmml\" xref=\"p1.1.m1.1.3.2\">d</ci>\n            <apply id=\"p1.1.m1.1.3.3.cmml\" xref=\"p1.1.m1.1.3.3\">\n              <times id=\"p1.1.m1.1.3.3.3.cmml\" xref=\"p1.1.m1.1.3.3.3\"/>\n              <ci id=\"p1.1.m1.1.3.3.1.cmml\" xref=\"p1.1.m1.1.3.3.1\">d</ci>\n              <ci id=\"p1.1.m1.1.3.3.2.cmml\" xref=\"p1.1.m1.1.3.3.2\">𝑡</ci>\n            </apply>\n          </apply>\n          <apply id=\"p1.1.m1.1.4.cmml\" xref=\"p1.1.m1.1.4\">\n            <divide id=\"p1.1.m1.1.4.1.cmml\" xref=\"p1.1.m1.1.4\"/>\n            <apply id=\"p1.1.m1.1.4.2.cmml\" xref=\"p1.1.m1.1.4.2\">\n              <partialdiff id=\"p1.1.m1.1.4.2.1.cmml\" xref=\"p1.1.m1.1.4.2.1\"/>\n              <csymbol cd=\"latexml\" id=\"p1.1.m1.1.4.2.2.cmml\" xref=\"p1.1.m1.1.4.2.2\">Q505735</csymbol>\n            </apply>\n            <apply id=\"p1.1.m1.1.4.3.cmml\" xref=\"p1.1.m1.1.4.3\">\n              <partialdiff id=\"p1.1.m1.1.4.3.1.cmml\" xref=\"p1.1.m1.1.4.3.1\"/>\n              <apply id=\"p1.1.m1.1.4.3.2.cmml\" xref=\"p1.1.m1.1.4.3.2\">\n                <ci id=\"p1.1.m1.1.4.3.2.1.cmml\" xref=\"p1.1.m1.1.4.3.2.1\">˙</ci>\n                <apply id=\"p1.1.m1.1.4.3.2.2.cmml\" xref=\"p1.1.m1.1.4.3.2.2\">\n                  <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.4.3.2.2.3.cmml\" xref=\"p1.1.m1.1.4.3.2.2\">subscript</csymbol>\n                  <csymbol cd=\"latexml\" id=\"p1.1.m1.1.4.3.2.2.1.cmml\" xref=\"p1.1.m1.1.4.3.2.2.1\">Q505735</csymbol>\n                  <ci id=\"p1.1.m1.1.4.3.2.2.2.1.cmml\" xref=\"p1.1.m1.1.4.3.2.2.2.1\">𝑖</ci>\n                </apply>\n              </apply>\n            </apply>\n          </apply>\n        </apply>\n      </apply>\n    </annotation-xml>\n    <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">{\\partial{L}\\over\\partial q_{i}}={\\mathrm{d}\\over\\mathrm{d}t}{\\partial{L}\\over%\n\\partial{\\dot{q_{i}}}}</annotation>\n  </semantics>\n</math>",
  "uri" : "https://en.formulasearchengine.com/w/index.php?oldid=24328#math24328.67",
  "title" : "Lagrangian_mechanics",
  "type" : "equation"
}