The Characterization of the Variational Minimizers for Spatial Restricted N+1-Body Problems
We use Jacobi's necessary condition for the variational minimizer to study the periodic solution for spatial restricted N+1-body problems with a zero mass on the vertical axis of the plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or odd symmetric...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/845795 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566771685523456 |
|---|---|
| author | Fengying Li Shiqing Zhang Xiaoxiao Zhao |
| author_facet | Fengying Li Shiqing Zhang Xiaoxiao Zhao |
| author_sort | Fengying Li |
| collection | DOAJ |
| description | We use Jacobi's necessary condition for the variational minimizer to study the periodic solution for spatial restricted N+1-body problems with a zero mass on the vertical axis of the plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or odd symmetric loop space must be a nonconstant periodic solution for any 2≤N≤472; hence the zero mass must oscillate, so that it cannot be always in the same plane with the other bodies. This result contradicts with our intuition that the small mass should always be at the origin. |
| format | Article |
| id | doaj-art-9765aee2e4ab4217ae038583be72290a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9765aee2e4ab4217ae038583be72290a2025-02-03T01:03:13ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/845795845795The Characterization of the Variational Minimizers for Spatial Restricted N+1-Body ProblemsFengying Li0Shiqing Zhang1Xiaoxiao Zhao2Yangtze Center of Mathematics and College of Mathematics, Sichuan University, Chengdu 610064, ChinaYangtze Center of Mathematics and College of Mathematics, Sichuan University, Chengdu 610064, ChinaYangtze Center of Mathematics and College of Mathematics, Sichuan University, Chengdu 610064, ChinaWe use Jacobi's necessary condition for the variational minimizer to study the periodic solution for spatial restricted N+1-body problems with a zero mass on the vertical axis of the plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or odd symmetric loop space must be a nonconstant periodic solution for any 2≤N≤472; hence the zero mass must oscillate, so that it cannot be always in the same plane with the other bodies. This result contradicts with our intuition that the small mass should always be at the origin.http://dx.doi.org/10.1155/2013/845795 |
| spellingShingle | Fengying Li Shiqing Zhang Xiaoxiao Zhao The Characterization of the Variational Minimizers for Spatial Restricted N+1-Body Problems Abstract and Applied Analysis |
| title | The Characterization of the Variational Minimizers for Spatial Restricted N+1-Body Problems |
| title_full | The Characterization of the Variational Minimizers for Spatial Restricted N+1-Body Problems |
| title_fullStr | The Characterization of the Variational Minimizers for Spatial Restricted N+1-Body Problems |
| title_full_unstemmed | The Characterization of the Variational Minimizers for Spatial Restricted N+1-Body Problems |
| title_short | The Characterization of the Variational Minimizers for Spatial Restricted N+1-Body Problems |
| title_sort | characterization of the variational minimizers for spatial restricted n 1 body problems |
| url | http://dx.doi.org/10.1155/2013/845795 |
| work_keys_str_mv | AT fengyingli thecharacterizationofthevariationalminimizersforspatialrestrictedn1bodyproblems AT shiqingzhang thecharacterizationofthevariationalminimizersforspatialrestrictedn1bodyproblems AT xiaoxiaozhao thecharacterizationofthevariationalminimizersforspatialrestrictedn1bodyproblems AT fengyingli characterizationofthevariationalminimizersforspatialrestrictedn1bodyproblems AT shiqingzhang characterizationofthevariationalminimizersforspatialrestrictedn1bodyproblems AT xiaoxiaozhao characterizationofthevariationalminimizersforspatialrestrictedn1bodyproblems |