{ "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" : "\n \n \n \n \n ∂\n ⁡\n L\n \n \n ∂\n ⁡\n \n q\n i\n \n \n \n =\n \n \n d\n \n d\n ⁢\n t\n \n \n ⁢\n \n \n ∂\n ⁡\n L\n \n \n ∂\n ⁡\n \n \n q\n i\n \n ˙\n \n \n \n \n \n \n \n \n \n \n \n \n Q505735\n \n \n \n \n subscript\n Q505735\n 𝑖\n \n \n \n \n \n \n \n d\n \n \n d\n 𝑡\n \n \n \n \n \n \n Q505735\n \n \n \n \n ˙\n \n subscript\n Q505735\n 𝑖\n \n \n \n \n \n \n \n {\\partial{L}\\over\\partial q_{i}}={\\mathrm{d}\\over\\mathrm{d}t}{\\partial{L}\\over%\n\\partial{\\dot{q_{i}}}}\n \n", "uri" : "https://en.formulasearchengine.com/w/index.php?oldid=24328#math24328.67", "title" : "Lagrangian_mechanics", "type" : "equation" }