กลศาสตร, แบบลากรองจ, งกฤษ, lagrangian, machanics, เป, นกลศาสตร, แบบหน, งท, อย, ภายในขอบเขตของกลศาสตร, งเด, งกฤษ, classical, machanics, เช, นเด, ยวก, บกฎของน, วต, งกฎข, อท, สองของน, วต, นสามารถทำนายการเคล, อนท, ของว, ตถ, โดยม, วใจสำค, การหาแรงล, พธ, กระทำต, อว,. klsastraebblakrxngc xngkvs Lagrangian Machanics epnklsastraebbhnungthixyuphayinkhxbekhtkhxngklsastrdngedim xngkvs Classical Machanics echnediywkbkdkhxngniwtn sungkdkhxthisxngkhxngniwtnsamarththanaykarekhluxnthikhxngwtthuodymihwicsakhy khux karhaaernglphththikrathatxwtthu aelaodythwippyhathangklsastrmikhwamsbsxnkhxnkhangmak echnkarekhluxnthikhxngwtthubnphiwthrngklm emuxkarkhanwnhaaernglphthmikhwamyaklabak klsastrkhxngniwtncungimehmaasmthicanamasuksaklsastrthimikhwamsbsxnid aenwkhiddanklsastraebbihmthiekhamaxthibayklsastrthimikhwamsbsxn khux klsastrlakrxngc thukesnxinpi 1788 ody nkkhnitsastrchawfrngess xitali ochaesf hluys lakrxngch karkhanwnaebbklsastrlakrxngcsamarthnaipprayuktichkbkarekhluxnthiaebbtang 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d t L q j L q j displaystyle 0 frac d dt left frac partial mathcal L partial dot q j right frac partial mathcal L partial q j ody q j displaystyle q j khuxphikdthwip generalized coordinate khxngrabb caehnsmkarlakrxngc sungekiywkhxngkbkdxnurksphlngnganaelaepnseklar aetktangcaksmkarkhxngniwtnsungekiywkhxngkbaerngaelaepnprimanewketxrthvsdikaraekwngkwdepnmumnxy aekikhthvsdikaraekwngkwdepnmumnxy xasyaenwkhidphunthanmacaksmkarkarekhluxnthikhxnglakrxngc smkarkarekhluxnthikhxnghamiltn xnukrmethyelxr aelakdkarekhluxnthikhxngniwtn odyichemtriksethnesxrinkaraekpyha ephuxthicaekhaicthvsdikaraekwngkwdepnmumnxy eracaepntxngrukhwamsmphnthkhxngphlngnganskykbkarsmdul wadwyenguxnikhkhxngkaresthiyrkhxngrabb sungepnphunthanthicaekhainthvsdini sungsamarthprayuktichkbkarekhluxnthiaebbesthiyr emuxrabbsmduleracaidwa Q k V q k 0 displaystyle Q k frac partial mathbf V partial q k 0 1 smkarthi 1 aesdngphlngngansky V mi extremun value inrabbthismdul srupidwaphawasmdulesthiyrekidkhun 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displaystyle V 0 makthisudtha d 2 V d q 2 0 displaystyle frac d 2 mathbf V dq 2 0 eracatxngphicarnaxnuphnththisungkhunip khux 1 smdulesthiyr emux d n V d q n gt 0 displaystyle frac d n mathbf V dq n gt 0 thi n gt 2 epncanwnkhu 2 smdulimesthiyr emux d n V d q n displaystyle frac d n mathbf V dq n 0 thi n gt 2 epncanwnkhi aela smdulimesthiyr emux d n V d q n lt 0 displaystyle frac d n mathbf V dq n lt 0 thi n gt 0 aelaepncanwnkhu karprayuktichthvsdikaraekwngkwdepnmumnxy samarthnaipxthibaykarekhluxnthikhxngluktumthitidmwlmakkwahnung hruxwtthutidspring hruxwtthuthimikarsnepnaexmplicudnxythvsdikarsnxyangelknxy Small oscillation inkaraekikhpyhabangpyhathimikhwamsbsxncneraimsamarthhaphlechlykhxngsmkarxnuphnthephuxxthibaylksnakarekhluxnthiid cungmiwithikarthicapramanlksnakarekhluxnthiodyphicarnnalksnakarekhluxnthirxb cudsmdul Equilibrium position karekhluxnthiinlksnani eriykwa karsnxyangelknxy Small oscillation 2 thvsdikarsnxyangelknxyphbtwxyangkarichnganthangdankayphaphxyangaephrhlayinkhwamrueruxngesiyng Acoustics karaephrngsikhxngomelkul Molecular spectra aelawngcrkhukhwb Coupled electrical circuit bthkhwamekiywkbfisiksniyngepnokhrng khunsamarthchwywikiphiediyidodyephimkhxmul duephimthi sthaniyxy fisikscakklsastrniwtnsuklsastrlakrxngc aekikhktkhxngniwtn Isaac Newton 1642 1727 ephuxkhwameriybngay kdkhxngniwtnsamarthxthibaysahrbxnuphakhhnung odythiimmikarsuyesiymwlmaknk sahrbrabbkhxngxnuphakh N smkarehlaniichkbxnuphakhaetlatwinrabb smkarkarekhluxnthikhxngxnuphakhkhxngmwl m khuxkdkhxthisxngkhxng Newton inpi kh s 1687 sungepnkarichsykrnewketxrsmyihm n khnann F m a displaystyle mathbf F m mathbf a emux a khuxkhwamerng aela F khuxaernglphth thikrathakbrabb sungxyuinrabb 3 miti aelwrabbnicarwmkbsmkarechingxnuphnthsamyephuxichinkaraekpyha enuxngcakmismkarewkhetxrthngsamtwepnxngkhprakxb karaekpyhakhux taaehnngkhxngewkhetxr r khxngxnuphakhinewla t karaekpyhathimi R epnewketxrtaaehnngkhxngxnuphakhthiewla t phayitenguxnikherimtnkhxng r aela v emux t 0 kdkhxngniwtnepneruxngngaythicathamaphicarnaichinphikdkharthiesiyn aetphikdkharthiesiynkimsadwkesmxip aelasahrbrabbphikdxun karichsmkarkarekhluxnthikhxngniwtncaklayepneruxngsbsxn inchudkhxng phikdechingesnokhng curvilinear coordinates 3 31 32 33 kdindrrchniethnesxr tensor khuxfxrmaebblakrxngc 3 4 F a m d 2 3 a d t 2 G a b c d 3 b d t d 3 c d t d d t T 3 a T 3 a 3 a d 3 a d t displaystyle F a m left frac mathrm d 2 xi a mathrm d t 2 Gamma a bc frac mathrm d xi b mathrm d t frac mathrm d xi c mathrm d t right frac mathrm d mathrm d t frac partial T partial dot xi a frac partial T partial xi a quad dot xi a equiv frac mathrm d xi a mathrm d t inkrnithi Fa epnswnprakxbkhwamimaeprphn khxngaerngthiekidkhunkbxnuphakh Gabc epnsylksn Christoffel khxngchnidthisxng T 1 2 m g b c d 3 b d t d 3 c d t displaystyle T frac 1 2 mg bc frac mathrm d xi b mathrm d t frac mathrm d xi c mathrm d t epnphlngnganclnkhxngxnuphakh aela gbc epnswnprakxbthiaeprprwnkhxngemtriksethnesxrkhxngrabbphikdaebbokhng dchnithnghmd a b c aetlakhacamikha 1 2 3 sungphikdesnokhngimehmuxnknkbphikdthwip mnxaccaduehmuxnepneruxngthiekidkhunmakekinipthicaoynkdhmaykhxngniwtninrupaebbni aetkmikhxidepriyb swnprakxbkhxngkarernginaengkhxngsylksn Christoffel samarthhlikeliyngid odykarpraeminxnuphnthkhxngphlngnganclnaethn thaimmiaerngthiekidkhunkbxnuphakh khux F 0 caimekidkarerng aetcaekhluxnthidwykhwamerwkhngthiepnesntrng inthangkhnitsastrkaraekpyhakhxngsmkarechingxnuphnthkhux geodesics nnkhuxesnokhngkhxngkhwamyawsudkhidrahwangcudsxngcudinphunthi sungxaccanxythisud dngnnkhuxesnthangthisnthisud aetkimcaepn inphunthicringthiwangepla aebb 3D geodesics caepnesntrngethann dngnnsahrbxnuphakhxisra kdkhxthisxngkhxngniwtncungekidkhunphrxmkbsmkareching geodesic aelarabuxnuphakhxisratam geodesics sungepnwithikhidsudthisamarthekhluxnthiipid thaxnuphakhtkxyuphayitaerngthi F 0 xnuphakhcamikhwamerngkhunenuxngcakaerngthikrathatxmn aelacaxxkipcak geodesics thicaptibtitamthaepnxisra dwykhwamehmaasmkhxngprimanthikahndiwinthirabaebbaebndewirkh 3 miti cnthungkalxwkasokhng 4 miti rupaebbkhangtnkhxngkdniwtncanamasuthvsdismphththphaphthwipkhxngixnsitnsunginkrninixnuphakhxisracatam geodesics inswnokhng space time sungimmi esntrng krnisamy xyangirktamerayngcaepntxngthrabphlrwmkhxngaerng F thikrathakbxnuphakh sungcatxngichaerngthiimmikhxcakd bwkkbaerngthimikhxcakd C F C N displaystyle mathbf F mathbf C mathbf N aerngkhxcakd xacmikhwamsbsxn enuxngcakodythwipaelwcakhunxyukbewla nxkcaknithamikhxcakd khxbekhtphikdimidepnxisra aetekiywkhunkbsmkarkhxcakdxyangnxyhnungkhx aerngkhxcakd samarththukkacdxxkcaksmkarkhxngkarekhluxnthi cungthaih aerngthiimmikhxcakdcakhngxyu hruxrwmxyuinsmkar khxcakdkhxngsmkarkarekhluxnthi suthi buychwy 2556 klsastrkhlassik phimkhrngthi 1 krungethph sankphimphmhawithyalyekstrsastr suthi buychwy 2556 klsastrkhlassik phimkhrngthi 1 krungethph sankphimphmhawithyalyekstrsastr suthi buychwy 2556 klsastrkhlassik phimkhrngthi 1 krungethph sankphimphmhawithyalyekstrsastr suthi buychwy 2556 klsastrkhlassik phimkhrngthi 1 krungethph sankphimphmhawithyalyekstrsastr Schuam 1988 p 156 Synge amp Schild 1949 p 150 152ekhathungcak https th wikipedia org w index php title klsastraebblakrxngc amp oldid 9215836, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,