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The contact geometry of circular spatial restricted 3-body problem : 제한된 원형 3차원 3체문제의 접촉기하
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Otto van Koert | - |
dc.contributor.author | 조완기 | - |
dc.date.accessioned | 2019-10-21T03:38:41Z | - |
dc.date.available | 2019-10-21T03:38:41Z | - |
dc.date.issued | 2019-08 | - |
dc.identifier.other | 000000156966 | - |
dc.identifier.uri | https://hdl.handle.net/10371/162421 | - |
dc.identifier.uri | http://dcollection.snu.ac.kr/common/orgView/000000156966 | ko_KR |
dc.description | 학위논문(박사)--서울대학교 대학원 :자연과학대학 수리과학부,2019. 8. Otto van Koert. | - |
dc.description.abstract | In this thesis, we consider the spatial restricted three-body problem and show that the energy hypersurface are of contact type whenever the energies lies on the range below and slightly above the first critical value. If the energy is slightly above the first critical value case, we consider a Liouville vector field on small neighborhood of the first Lagrange point. The Moser's regularization gives a compactification of the regularized hypersurface and this regularized hypersurface is diffeomorphic to the unit contangent bundle of 3-sphere. Because of this regularization, we can show that there is no blue sky catastrophe on this regularized energy hypersurface. | - |
dc.description.abstract | 본 학위논문에서는 제한된 3차원 3체문제를 건설한 후 그 초곡면이 접촉구조(contact structure)를 가짐을 증명한다. 이 증명은 에너지 레벨이 첫번째 특이값보다 낮거나 살짝 높은 레벨에서 유효하다. 이는 Liouville 벡터장이 주어진 초곡면에 가로놓인다는(transverse)점을 증명함으로써 보일수 있다. 그러나 이와같은 초곡면은 두 물체의 충돌(collision)의 존재 때문에 compact 하지 않다. 이러한 상황에서 Moser의 정규화를 이용하면 주어진 초곡면 대신 compact한 초곡면에서 역학을 생각할수 있다. 또한 이러한 정규화 덕분에 3차원 3체 문제에선 blue sky catastrophe가 존재하지 않음을 보일수 있다. | - |
dc.description.tableofcontents | Contents
Abstract 1 Introduction 1 2 Preliminaries 7 2.1 Equation of Motion and Hamiltonian System . . . . . . . . . . . 7 2.2 Symplectic manifolds and Hamiltonian . . . . . . . . . . . . . . 9 2.3 Contact manifolds and Liouville vector field . . . . . . . . . . . 14 3 The restricted three body problem and rotating Kepler problem 17 3.1 The spatial restricted three body problem . . . . . . . . . . . . 18 3.1.1 The spatial restricted three body problem in rotating frame 18 3.1.2 Lagrange points and critical points of Effective potential 20 3.1.3 The Hills region . . . . . . . . . . . . . . . . . . . . . . 27 3.2 The planar Kepler problem and integrable system . . . . . . . . 29 3.2.1 Integrable Hamiltonian system . . . . . . . . . . . . . . . 29 3.2.2 The Kepler problem . . . . . . . . . . . . . . . . . . . . 31 3.3 The rotating Kepler problem and its dynamics . . . . . . . . . . 35 4 Regularization on celestial mechanics 37 4.1 Mosers regularization on celestial mechanics . . . . . . . . . . . 38 4.2 Levi-civita regularization of energy hypersurface . . . . . . . . . 43 5 The spatial restricted three body problem and contact geometry 47 5.1 Minimum of effective potential U on radius fixed sphere . . . . . 48 5.2 Transversality of spatial restricted three body problem . . . . . . . . 57 6 Connected sum of hypersurface in spatial case 63 7 Mosers regularization of spatial restricted three body problem 71 7.1 The stereographic projection and transforming of the Hamiltonian 72 7.2 Transversality of regularized energy hypersurface . . . . . . . . 74 8 Blue sky catastrophes 78 Abstract (in Korean) 84 Acknowledgement (in Korean) 85 | - |
dc.language.iso | eng | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | circular spatial restricted three body problem | - |
dc.subject | Hamiltonian dynamics | - |
dc.subject | effective potential | - |
dc.subject | regularization | - |
dc.subject | Hill's region | - |
dc.subject.ddc | 510 | - |
dc.title | The contact geometry of circular spatial restricted 3-body problem | - |
dc.title.alternative | 제한된 원형 3차원 3체문제의 접촉기하 | - |
dc.type | Thesis | - |
dc.type | Dissertation | - |
dc.contributor.AlternativeAuthor | Cho WanKi | - |
dc.contributor.department | 자연과학대학 수리과학부 | - |
dc.description.degree | Doctor | - |
dc.date.awarded | 2019-08 | - |
dc.identifier.uci | I804:11032-000000156966 | - |
dc.identifier.holdings | 000000000040▲000000000041▲000000156966▲ | - |
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