A Minimizing Property of Lagrangian Solutions
被引量：3
A Minimizing Property of Lagrangian Solutions
摘要
In this paper,we prove that the Lagrangian solutions to the three-body problem minimize the action function.
In this paper,we prove that the Lagrangian solutions to the three-body problem minimize the action function.
基金
The first author is partially supported by a grant of NNSFC
The second author is partially supported by grants of MOSTC
NNSFC
QSSTF
参考文献6
-
1LONG Yiming and ZHANG Shiqing1. Nankai Institute of Mathematics , Nankai University , Tianjin 300071 , China ,2. Department of Applied Mathematics, Chongqing University, Chongqing 400044, China Associate Member of the ICTP..Geometric characterizations for variational minimization solutions of the 3-body problem[J].Chinese Science Bulletin,1999,44(18):1653-1655. 被引量：2
-
2Gordon W.A minimizing property of Keplerian orbits[].American Journal of Mathematics.1977
-
3Va?s?l?,J.Lectures on n-Dimensional Quasiconformal Mappings[].Lecture Notes in Mathematics.1971
-
4H. Pollard.Celestial Mechanics[]..1976
-
5Chenciner, A,Desolneux, N.Minima de l’’ integrale d’’ action et equilibres relatifs de n corps[].C R Acad Sci Paris se-rie I.1998
-
6Abraham,R.,Marsden,J.E. Foundations of Mechanics . 1978
二级参考文献13
-
1Enrico Serra,Susanna Terracini.Collisionless periodic solutions to some three-body problems[J]. Archive for Rational Mechanics and Analysis . 1992 (4)
-
2Vittorio Coti Zelati.A class of periodic solutions of the N-body problem[J]. Celestial Mechanics and Dynamical Astronomy . 1989 (2)
-
3Rabinowitz,P.H.Periodic solutions of Hamiltonian systems. Communications of the ACM . 1978
-
4Ambrosetti,A.,Zelati,V. Coti. Periodic solutions of singular Lagrangian systems . 1993
-
5U. Bessi,V. Coti Zelati.Symmetries and noncollision closed orbits for planar N-body-type problems. Nonlinear Analysis . 1991
-
6Coti Zelati,V.The periodic solutions of N–body type problems. Ann. IHP. Anal. nonlinear . 1990
-
7Coti Zelati,V.A class of periodic solutions for the N-body problem. Celestial Mechanics . 1989
-
8Serra E,Terracini S.Collisionless periodic solutions to some three-body problems. Archive for Rational Mechanics and Analysis . 1992
-
9SIEGLE C,MOSER J.Lectures on Celestial Mechanics. . 1971
-
10Gordon,W.A minimizing property of Keplerian orbits, Amer. Journal of Mathematical . 1977
同被引文献4
-
1张世清,周青.Variational methods for the choreography solution to the three-body problem[J].Science China Mathematics,2002,45(5):594-597. 被引量：7
-
2DING Yanheng LI Shujie (Institute of Mathematics,Academia Sinica,Beijing 100080,China).A REMARK ON PERIODIC SOLUTIONS OF SINGULAR HAMILTONIAN SYSTEMS WITH SUBLINEAR TERMS[J].Systems Science and Mathematical Sciences,1992,5(2):121-126. 被引量：1
-
3Zhang Shiqing,Zhou Qing.Symmetric Periodic Noncollision Solutions for N-Body-Type Problems[J].Acta Mathematica Sinica,English Series,1995,11(1):37-43. 被引量：1
-
4Yiming Long Nankai Institute of Mathematics. Nankai University. Tianjin 300071. P. R. China Shiqing Zhang Department of Applied Mathematics Chongqing University. Chongqing 40004, P.R. China.Geometric Characterizations for Variational Minimization Solutions of the 3-Body Problem[J].Acta Mathematica Sinica,English Series,2000,16(4):579-592. 被引量：3
引证文献3
-
1DENG ChunHua 1,2 , ZHANG ShiQing 1, & ZHOU Qing 3 1 Yangtze Center of Mathematics and College of Mathematics, Sichuan University, Chengdu 610064, China,2 Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an 223001, China,3 Department of Mathematics, East China Normal University, Shanghai 200062, China.Rose solutions with three petals for planar 4-body problems[J].Science China Mathematics,2010,53(12):3085-3094.
-
2邓义杨.固定三中心的四体问题的三叶型周期解[J].绵阳师范学院学报,2013,32(5):4-7.
-
3Fengying LI,Shiqing ZHANG.Periodic Solutions for N-Body-Type Problems[J].Chinese Annals of Mathematics,Series B,2020,41(5):733-740.
-
1朱如曾,向程.STUDIES OF MELNIKOV METHOD AND TRANSVERSAL HOMOCLINIC ORBITS IN THE CIRCULAR PLANAR RESTRICTED THREE－BODY PROBLEM[J].Applied Mathematics and Mechanics(English Edition),1996,17(12):1177-1187.
-
2林祁斜,任中洲.Three-Body Problem of H_2^+ Ion[J].Communications in Theoretical Physics,2012,57(2):214-216.
-
3马中骐.Quantum three-body problems[J].Science China Mathematics,2000,43(10):1093-1107.
-
4张世清,周青.Variational methods for the choreography solution to the three-body problem[J].Science China Mathematics,2002,45(5):594-597. 被引量：7
-
5Atsushi Ichimura.THREE-BODY SCATTERING CROSS SECTION AND SINGULARITIES OF THE T-MATRIX[J].原子与分子物理学报,1990,7(4):1614-1617.
-
6H. Sadeghi H. Khalili.Three-Body Calculation of the 4He（aH,γ）7Li and 4He（aHe,γ）7Be Reactions and Structure of the 7Li and 7Be at Solar Energies[J].Chinese Physics Letters,2014,31(1):56-60. 被引量：1
-
7LI XiaoMing,LIAO ShiJun.On the stability of the three classes of Newtonian three-body planar periodic orbits[J].Science China(Physics,Mechanics & Astronomy),2014,57(11):2121-2126. 被引量：3
-
8Yuan Jian Liu Xiaodong Xu Guoji Sun Zuxun China Institute of Atomic Energy,Beijing 102413Lin Erhkang Wang Changwan Yu Yuehchung Liu Tongyuan Institute of Physics,Academia Sinica,Taipei 11529Tang Guoyou Shi Zhaomin Chen Jinxiang Gong Linghua Yang Qixiang Institute of Heavy Ion Physics,Peking University,Beijing 100871Zhang Peihua Graduate School,the Chinese Academy of Sciences,P.O.Box 3908,Beiting 100039.Spectra of p-^(11)B Three-Body Sequential Decay Reaction[J].Chinese journal of nuclear physics,1997(4):220-225.
-
9吴雷,张解放.Modulational Instability of （1 ＋ 1）-Dimensional Bose-Einstein Condensate with Three-Body Interatomic Interaction[J].Chinese Physics Letters,2007,24(6):1471-1474. 被引量：1
-
10K.P.Khemchandani,A.Martínez Torres,E.Oset.Three-body hadronic molecules[J].Chinese Physics C,2010,34(9):1286-1289.
