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The FreeFall ThreeBody Problem : Escape and Collision
https://ir.soken.ac.jp/records/373
https://ir.soken.ac.jp/records/37362550e582ec74161b7728f1a77cb8003
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要旨・審査要旨 / Abstract, Screening Result (266.0 kB)


本文 (23.1 MB)

Item type  学位論文 / Thesis or Dissertation(1)  

公開日  20100222  
タイトル  
タイトル  The FreeFall ThreeBody Problem : Escape and Collision  
タイトル  
言語  en  
タイトル  The FreeFall ThreeBody Problem : Escape and Collision  
言語  
言語  eng  
資源タイプ  
資源タイプ識別子  http://purl.org/coar/resource_type/c_46ec  
資源タイプ  thesis  
著者名 
梅原, 広明
× 梅原, 広明


フリガナ 
ウメハラ, ヒロアキ
× ウメハラ, ヒロアキ


著者 
UMEHARA, Hiroaki
× UMEHARA, Hiroaki


学位授与機関  
学位授与機関名  総合研究大学院大学  
学位名  
学位名  博士（理学）  
学位記番号  
内容記述タイプ  Other  
内容記述  総研大甲第316号  
研究科  
値  数物科学研究科  
専攻  
値  09 天文科学専攻  
学位授与年月日  
学位授与年月日  19980324  
学位授与年度  
1997  
要旨  
内容記述タイプ  Other  
内容記述  The escape phenomena in the threebody problem with zero initial velocities and equal masses are studied both numerically and analytically. In particular, the effects of triple and binary collisions are considered in detail. Here, escape means that two particles form a binary and the third particle recedes from the binary to infinity. Collision is defined as the event when the distance between particles vanishes. First, escape orbits are searched by a numerical survey of the initialvalue space and compared with collision orbits obtained by Tanikawa et al. (Cele. Mech. Dyna. Astr., 62 (1995) 335362). Most escape phenomena occur after the triple encounter which is of the slingshot type. A particle passes through between the other particles which are receding from each other. It is found that escape orbits due to slingshot distribute around a particular family of binarycollision orbits which maintains nearly isosceles configuration. The configuration and the velocity vectors are almost symmetric. Moreover, if orbits approach sufficiently close to triple collision, all escape orbits distribute around the binarycollision orbits. Furthermore, orbits without escape during the first triple encounter are also found sufficiently close to the triplecollision orbit. Therefore, it becomes clear that explaining the distribution of escape orbits only by triplecollision orbits is impossible. The particular family of binary collisions has a central role in escape phenomena as well as triple collision does. Discovery of escape orbits due to exchange encounter is also one of the results. Two close approaches between two particles successively occur. The dynamical features of the slingshot and the exchange are compared with each other. Escape probabilities and increments of binding energies are evaluated statistically for the respective encountertypes. It is shown that some of slingshot encounters result in more energetic evolution than all of exchange encounters. So the restrictive and the favorable conditions of slingshot configurations leading to escape are searched for. Using the slingshot conditions, it is answered why slingshotescape orbits distribute around the particular binarycollision orbits showing nearly symmetrical motion. Finally, it is proved analytically that both escape and nonescape orbits after the first triple encounter exist arbitrarily close to the particular triplecollision orbit. The homotheticequilateral triplecollision orbit is considered. This orbit maintains the equilateraltriangle configuration. It is proved that in the initialvalue space escape orbits distribute around three kinds of isosceles orbits where different particles escape and nonescape orbits are distributed in between. In order to show this, it is proved that the homotheticequilateral orbit is isolated from other triplecollision orbits so far as the collision during the first triple encounter concerns. Moreover, the escape criterion is formulated in the planar isosceles problem and translated into the words of regularizing variables. The results explain the orbital structure numerically obtained in the beginning of the present thesis. With the aid of numerical integrations, it is shown that the distribution of escape orbits around another triplecollision orbit are topologically similar to the one around the homotheticequilateral orbit. Here, it is found that the isosceles motion has an important role in determining the dynamical evolution. 

所蔵  
値  有  
フォーマット  
内容記述タイプ  Other  
内容記述  application/pdf  
著者版フラグ  
出版タイプ  AM  
出版タイプResource  http://purl.org/coar/version/c_ab4af688f83e57aa 