Hamiltonian mechanics and Symmetries

Hamiltonian mechanics;Integrable system;Kepler problem;Angular momentum;Moment map;해밀턴계;적분가능계;케플러 문제;각운동량;운동량 사상;510

자연과학대학 수리과학부 ;

University:서울대학교 대학원

关键词: Hamiltonian mechanics;    Integrable system;    Kepler problem;    Angular momentum;    Moment map;    해밀턴계;    적분가능계;    케플러 문제;    각운동량;    운동량 사상;    510;   

Others  :  http://s-space.snu.ac.kr/bitstream/10371/131482/1/000000020676.pdf

美国|英语

来源: Seoul National University Open Repository

【 摘 要 】

The aim of this thesis is to understand the relation of symmetries and integralsof Hamiltonian system and their importance. We also treat an amazingstructure of an integrable system and moment maps to investigate equivalentHamiltonian systems. Through the paper, we study the Kepler problemin detail as the example to see how these concepts work in a concrete system.We show that the Kepler problem can be gured out by the angularmomentum of unit-speed geodesic circles on the unit-sphere.