Euler–Lagrange equation

English

Wikipedia has an article on:

Etymology

Named after Leonhard Euler (1707–1783), Swiss mathematician and physicist, and Joseph Louis Lagrange (1736–1813), French mathematician and astronomer — originally from Italy.

Noun

Euler–Lagrange equation (plural Euler–Lagrange equations)

1. (mechanics, analytical mechanics) A differential equation which describes a function $\mathbf{q}(t)$ which describes a stationary point of a functional, $S(\mathbf{q}) = \int L(t, \mathbf{q}(t), \mathbf{\dot q}(t))\,dt$, which represents the action of $\mathbf{q}(t)$, with $L$ representing the Lagrangian. The said equation (found through the calculus of variations) is ${\partial L \over \partial \mathbf{q}} = {d \over dt} {\partial L \over \partial \mathbf{\dot q}}$ 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.
↑Jump back a section
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8930202722549438, "perplexity_flag": "middle"}