"Euler-Lagrange equation" meaning in All languages combined

{
  "etymology_text": "Named after the Swiss mathematician and physicist Leonhard Euler (1707–1783), and the Italian-born French mathematician and astronomer Joseph Louis Lagrange (1736–1813).",
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    {
      "form": "Euler-Lagrange equations",
      "tags": [
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      "expansion": "Euler-Lagrange equation (plural Euler-Lagrange equations)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      "glosses": [
        "A differential equation which describes a function mathbf q(t) which describes a stationary point of a functional, S( mathbf q)=∫L(t, mathbf q(t), mathbf ̇q(t)),dt, which represents the action of mathbf q(t), with L representing the Lagrangian. The said equation (found through the calculus of variations) is ∂L/∂ mathbf q=d/dt∂L/∂ mathbf ̇q and its solution for mathbf q(t) represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action."
      ],
      "id": "en-Euler-Lagrange_equation-en-noun-qKchPddK",
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          "calculus of variations"
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      "qualifier": "analytical mechanics",
      "raw_glosses": [
        "(mechanics, analytical mechanics) A differential equation which describes a function mathbf q(t) which describes a stationary point of a functional, S( mathbf q)=∫L(t, mathbf q(t), mathbf ̇q(t)),dt, which represents the action of mathbf q(t), with L representing the Lagrangian. The said equation (found through the calculus of variations) is ∂L/∂ mathbf q=d/dt∂L/∂ mathbf ̇q and its solution for mathbf q(t) represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action."
      ],
      "topics": [
        "engineering",
        "mechanical-engineering",
        "mechanics",
        "natural-sciences",
        "physical-sciences"
      ],
      "wikipedia": [
        "Euler-Lagrange equation",
        "Joseph Louis Lagrange",
        "Leonhard Euler"
      ]
    }
  ],
  "word": "Euler-Lagrange equation"
}

{
  "etymology_text": "Named after the Swiss mathematician and physicist Leonhard Euler (1707–1783), and the Italian-born French mathematician and astronomer Joseph Louis Lagrange (1736–1813).",
  "forms": [
    {
      "form": "Euler-Lagrange equations",
      "tags": [
        "plural"
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      "glosses": [
        "A differential equation which describes a function mathbf q(t) which describes a stationary point of a functional, S( mathbf q)=∫L(t, mathbf q(t), mathbf ̇q(t)),dt, which represents the action of mathbf q(t), with L representing the Lagrangian. The said equation (found through the calculus of variations) is ∂L/∂ mathbf q=d/dt∂L/∂ mathbf ̇q and its solution for mathbf q(t) represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action."
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      "qualifier": "analytical mechanics",
      "raw_glosses": [
        "(mechanics, analytical mechanics) A differential equation which describes a function mathbf q(t) which describes a stationary point of a functional, S( mathbf q)=∫L(t, mathbf q(t), mathbf ̇q(t)),dt, which represents the action of mathbf q(t), with L representing the Lagrangian. The said equation (found through the calculus of variations) is ∂L/∂ mathbf q=d/dt∂L/∂ mathbf ̇q and its solution for mathbf q(t) represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action."
      ],
      "topics": [
        "engineering",
        "mechanical-engineering",
        "mechanics",
        "natural-sciences",
        "physical-sciences"
      ],
      "wikipedia": [
        "Euler-Lagrange equation",
        "Joseph Louis Lagrange",
        "Leonhard Euler"
      ]
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  "word": "Euler-Lagrange equation"
}