Geometric formulation of Hamiltonian mechanics

Nazcv pra.ce: Gcometricka formulaee Ilamiltoiiovy mechaiiiky Autor: Robert Svarc Katedra (ustav): Osl.av teoretieke fyziky Vedouci bakalafsko prace: Doc.RNDr. Jin Podolsky, CSc. e-mail vedouciho: Jin. Podolsk ^hiiff. cuni.cz Abstrakt: V pfcdlo/eno praei stndnjome geometrickon formulae! Hamilto- uovy niecliauiky. Nejprve se zabyvame situaci, kdy hamiltouian ne/avisi na case. V tomto pfi'i)ade jo pfislusnou gconiotrickou arenou 2//-diinonziona.lni syniplokticka varieta. Naskvlno pfipmistimo casove zavisle ha.miltoniany a pfechii/iiiic na 2n -\ I dimeiizionalai ro/sirony lazovy prustor. Vyvoj mccha- uickeho systoniu jo v obon prij)adooh uroon intogralnimi kfivkami voktoro- voho pole, kloro jo dano Hainiltonovymi kanonickyini rovniconii. Pro oba pfijjady rovnoz zavadimo kanonicko transformace. Na znvor goomcticky in- terpretujein HainiltonovLi-Jacobiho rovnici. Title: Geometric formulation of Hamiltoiiian mecluuiics Author: Robert, Svarc Department: Institute of Theoretical Physics Supervisor: Doc.R.NDr. Jifi Podolskj', CSc. Supervisor's e-mail address: Jiri.PodolskyOmfl.cuni.cz Abstract: In this work we study geometric formulation of Ilamiltonian me- chanics. At the beginning wolook at situation, when the Hamiltoiiian function is time-independent. In this case our geometric arena, is the ^//-dimensional..