Duzhkami Puassona v klasichnij mehanici nazivayetsya viraz f g i 1 N f p i g q i f q i g p i displaystyle varphi g sum i 1 N left frac partial varphi partial p i frac partial g partial q i frac partial varphi partial q i frac partial g partial p i right de f displaystyle varphi j g displaystyle g bud yaki funkciyi uzagalnenih koordinat q i displaystyle q i ta uzagalnenih impulsiv p i displaystyle p i N displaystyle N kilkist stupeniv svobodi sistemi Puassonova duzhka ye klasichnim analogom kvantovogo komutatora Vlastivosti RedaguvatiVlastivosti sho viplivayut bezposeredno z matematichnogo oznachennya f g g f displaystyle f g g f nbsp a f b g h a f h b g h displaystyle alpha f beta g h alpha f h beta g h nbsp t f g f t g f g t displaystyle frac partial partial t f g frac partial f partial t g f frac partial g partial t nbsp f g h f h g f g h displaystyle fg h f h g f g h nbsp f g h g h f h f g 0 displaystyle f g h g h f h f g 0 nbsp totozhnist YakobiVazhlivoyu vlastivistyu duzhok Puasona ye yih invariantnist vidnosno kanonichnih peretvoren tobto vidnosno perehodu do novogo naboru kanonichnih zminnih Q 1 P N displaystyle Q 1 P N nbsp f g i N f P i g Q i f Q i g P i displaystyle varphi g sum i N left frac partial varphi partial P i frac partial g partial Q i frac partial varphi partial Q i frac partial g partial P i right nbsp Yaksho odna z funkcij zbigayetsya z uzagalnenim impulsom abo koordinatoyu todi otrimayemo f q i f p i displaystyle f q i frac partial f partial p i nbsp p i g g q i displaystyle p i g frac partial g partial q i nbsp Yaksho zaminiti i drugu funciyu q j q i p j p i 0 displaystyle q j q i p j p i 0 nbsp p j q i d j i displaystyle p j q i delta ji nbsp Ostanni tri totozhnosti umova kanonichnosti naboru zminnih q 1 p N displaystyle q 1 p N nbsp Kozhen integral ruhu ps displaystyle psi nbsp povinen zadovilnyati rivnyannyu ps t ps H 0 displaystyle frac partial psi partial t psi H 0 nbsp U vipadku koli ps displaystyle psi nbsp ne zalezhit vid chasu yavno H ps 0 displaystyle H psi 0 nbsp Zokrema z oglyadu na teoremu Liuvillya gustina staniv u fazovomu prostori r displaystyle rho nbsp povinna zadovilnyati rivnyannyu Liuvillya r t r H 0 displaystyle frac partial rho partial t rho H 0 nbsp Div takozh RedaguvatiMehanika Gamiltona Integral ruhu Duzhki LagranzhaDzherela RedaguvatiYezhov S M Makarec M V Romanenko O V Klasichna mehanika K VPC Kiyivskij universitet 2008 480 s Fedorchenko A M Teoretichna mehanika K Visha shkola 1975 516 s Otrimano z https uk wikipedia org w index php title Duzhki Puassona amp oldid 38785264
