svayambharanaadhikaaramillaatha mechanics

svayambharanamillaatha mechanics samayathe aasrayichulla parivarthanangalkku vidheyamaaya aapekshikamallaatha mechanical samvidaanangale vivarikkunnu. prathyekichum, ithu lagranchiyanmarum haamiltoniyanukalum samayathe aasrayikkunna mechanical samvidaanangalude kaaryamaan. svayambharanamallaatha mekkaaniksinte konfigareshan space formula _ 3 ekopippicha time axis formula _ 2-ll oru fiber bundle formula _ 1 aanu. 
eee bundle nissaaramaan, ennaal athinte vyathyastha nissaaravalkkarana soothravaakyam _ 4 vyathyastha noonn-relativistic reference frameukalude thiranjeduppumaayi poruthappedunnu. atharamoru reference framine oru kanakshan prathinidheekarikkunnu
eee nissaaravalkkaranavumaayi bandhappett formula 7 roopathil edukkunna formula 6-leeii formula 5. anubandha koveriyant deferential formula _ 8
oru reference frame formula _ 5 maayi bandhappett aapekshika vegatha nirnnayikkunnu.
thalphalamaayi, svayambharanaadhikaaramillaatha mechanics (prathyekichu, svayambharanaadhikaaramillaatha hamiltonian mechanics) formula 10-ll oru koveriyant classical feeld sidhaanthamaayi (prathyekichu koveriyant hamiltonian feeld sidhaantham) roopappeduthaan kazhiyum. athanusarichu, svayambharanaadhikaaramillaatha mekkaaniksinte vegatha ghattam space formula 1-nte jettu manifold formulayanu. hamiltonian noonn-autonomous mekkaaniksinte chalanathmakatha nirvachikkunnath hamiltonian phoom formula _ 17 aanu. 
formula 20 upayogichu ekopippikkukayum canonical symplectic roopam nalkukayum cheiyunna formula 19-nte kottaanjant bundle formula 18-ll thulyamaaya hamiltonian svayambharana samvidaanavumaayi oraalkk bandhappedutthaam; athinte hamiltonian formula 21 aanu.

