Qhov sib txawv tseem ceeb ntawm Lagrangian thiab Hamiltonian mechanics yog tias Lagrangian mechanics piav txog qhov sib txawv ntawm kinetic thiab muaj peev xwm energies, whereas Hamiltonian mechanics piav txog cov lej ntawm kinetic thiab muaj peev xwm energies.
Lagrangian mechanics thiab Hamiltonian mechanics yog cov ntsiab lus tseem ceeb hauv lub cev chemistry uas tuaj nyob rau hauv classical mechanics. Lub Lagrangian mechanics yog tsim los ntawm Italian mathematician Joseph-Louis Lagrange hauv 1788, thaum Hamiltonian mechanics tau tsim los ntawm William Rowan Hamilton hauv 1833.
Lagrangian Mechanics yog dab tsi?
Lagrangian mechanics tuaj yeem txhais tau tias yog kev hloov kho ntawm cov tshuab qub qub uas tau qhia los ntawm tus lej Italian hu ua Joseph-Louis Lagrange xyoo 1788. Nyob rau hauv lub tswv yim tshuaj no, txoj hauv kev ntawm lub cev uas muaj cov khoom yog muab los ntawm kev daws cov Lagrange sib npaug hauv ib qho ntawm ob hom: Lagrange sib npaug ntawm thawj hom thiab Lagrange sib npaug ntawm hom thib ob.
thawj hom Lagrange sib npaug kho cov kev txwv tshwj xeeb raws li kev sib npaug ntxiv siv Lagrange cov sib npaug, thaum thib ob ntawm Lagrange sib npaug suav nrog cov kev txwv ncaj qha los ntawm kev txiav txim siab ntawm kev sib koom ua ke. Txawm li cas los xij, nyob rau hauv ib qho ntawm ob hom no, ib qho kev ua lej hu ua Lagrangian raug xa mus rau kev ua haujlwm ntawm cov kev tswj xyuas dav dav, lawv lub sij hawm derivatives, thiab lub sij hawm. Ntxiv mus, lub tswv yim no muaj cov ntaub ntawv hais txog lub zog ntawm qhov system.
Daim duab 01: Joseph-Louis Lagrange
Lagrangian mechanics yog kev ua lej ntau dua thiab cov tswv yim tshuaj lom neeg. Tsis muaj lub tswv yim tshiab physics tau tsim nyog qhia rau daim ntawv thov ntawm Lagrangian mechanics thaum piv rau Newtonian mechanics. Txawm li cas los xij, Lagrangian mechanics yog qhov muaj txiaj ntsig zoo hauv kev daws cov teeb meem hauv physics thaum Newton's formulations ntawm classical mechanics tsis yooj yim.
Hamiltonian Mechanics yog dab tsi?
Hamiltonian mechanics yog ib qho kev ua lej zoo tshaj plaws ntawm classical mechanics. Lub tswv yim tshuaj no pab txhawb rau kev tsim cov statistical mechanics thiab quantum mechanics. Lub tswv yim no tau tsim los ntawm William Rowan Hamilton hauv xyoo 1833. Nws tau tsim nws los ntawm kev pib ntawm Lagrangian mechanics. Tsis tas li ntawd, Hamiltonian mechanics yog sib npaug rau Newton txoj cai ntawm kev txav mus los hauv cov kev txwv ntawm classical mechanics.
Daim duab 02: Sir William Hamilton
Hauv Hamiltonian mechanics, peb tuaj yeem siv cov txheej txheem canonical hauv kev piav qhia txog lub cev lub cev: r=(q, p). txhua qhov kev sib koom ua ke ntawm cov khoom no qi, pi yog ntsuas rau tus ncej ntawm kev siv ntawm lub cev ntawd. Lub qi kev sib koom ua ke yog lub npe hu ua kev tswj hwm dav dav, thaum pi yog lub npe hu ua lawv lub sijhawm sib koom ua ke.
Qhov txawv ntawm Lagrangian thiab Hamiltonian Mechanics yog dab tsi?
Lagrangian mechanics thiab Hamiltonian mechanics yog cov ntsiab lus tseem ceeb hauv lub cev chemistry uas tuaj nyob rau hauv classical mechanics. Lagrangian mechanics yog tsim los ntawm Italian mathematician hu ua Joseph-Louis Lagrange nyob rau hauv 1788, thaum Hamiltonian mechanics yog tsim los ntawm William Rowan Hamilton nyob rau hauv 1833. Qhov txawv tseem ceeb ntawm Lagrangian thiab Hamiltonian mechanics yog Lagrangian mechanics piav txog qhov sib txawv ntawm kinetic thiab muaj peev xwm energies, whereas. Hamiltonian mechanics piav txog qhov sib npaug ntawm kinetic thiab muaj peev xwm muaj zog. Tsis tas li ntawd, Lagrangian mechanics siv Cartesian kev tswj hwm hauv kev suav, hos Hamiltonian mechanics siv canonical coordinates.
Hauv qab no yog cov ntsiab lus ntawm qhov sib txawv ntawm Lagrangian thiab Hamiltonian mechanics hauv daim ntawv teev npe.
Summary – Lagrangian vs Hamiltonian Mechanics
Lagrangian mechanics tuaj yeem txhais tau tias yog kev hloov kho ntawm cov tshuab qub qub. Hamiltonian mechanics yog ib qho kev ua lej zoo tshaj plaws ntawm classical mechanics. Qhov sib txawv tseem ceeb ntawm Lagrangian thiab Hamiltonian mechanics yog tias Lagrangian mechanics piav txog qhov sib txawv ntawm kinetic thiab muaj peev xwm energies, whereas Hamiltonian mechanics piav txog cov kinetic thiab muaj peev xwm energies.
