See Euler-Lagrange equation on Wiktionary
{
"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"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Euler-Lagrange equation (plural Euler-Lagrange equations)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mechanics",
"orig": "en:Mechanics",
"parents": [
"Physics",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"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",
"links": [
[
"mechanics",
"mechanics"
],
[
"differential equation",
"differential equation"
],
[
"function",
"function"
],
[
"functional",
"functional"
],
[
"action",
"action"
],
[
"Lagrangian",
"Lagrangian"
],
[
"calculus of variations",
"calculus of variations"
],
[
"trajectory",
"trajectory"
],
[
"principle of least action",
"principle of least action"
]
],
"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"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Euler-Lagrange equation (plural Euler-Lagrange equations)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"Pages with 1 entry",
"Pages with entries",
"en:Mechanics"
],
"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."
],
"links": [
[
"mechanics",
"mechanics"
],
[
"differential equation",
"differential equation"
],
[
"function",
"function"
],
[
"functional",
"functional"
],
[
"action",
"action"
],
[
"Lagrangian",
"Lagrangian"
],
[
"calculus of variations",
"calculus of variations"
],
[
"trajectory",
"trajectory"
],
[
"principle of least action",
"principle of least action"
]
],
"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"
}
Download raw JSONL data for Euler-Lagrange equation meaning in All languages combined (2.3kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.