The topology of manifold M8 of the general three-body problem |
| |
| Affiliation: | 1. Department of Applied Physics, Lanzhou University of Technology, Lanzhou, Gansu 730050, PR China;2. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, PR China;3. School of Materials Science and Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, PR China;4. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, Gansu 730070, PR China;1. Department of Neonatology, Kasturba Medical College, Manipal, Manipal Academy of Higher Education (MAHE), Karnataka, India;2. Department of Pediatrics, Kasturba Medical College, Manipal, Manipal Academy of Higher Education (MAHE), Karnataka, India |
| |
| Abstract: | This paper studies the topology of manifold M8 of the general three-body problem, by means of a more elementary and intuitive method than that of S.Smale [3] and R.W.Easton [4,6]. The following results are independently obtained. - 1.1. G.D. Birkhoff's judgement [1] that the topology of M8 can vary only when the energy constant E passes through the admissible values of Lagrange's particular solutions is strictly proved.
- 2.2. The topologies of M8 when E lies in the five interals E>E0, E0>E>E1, E1>E>E2, E2>E>E3 and E<E3 are given completely, where E0 is the value corresponding to equilateral triangular solutions, whereas E1, E2 and E3 are values corresponding to collinear solutions.
- 3.3. The result in the paper of Dong Jin-zhu [5] about the connectedness of M8 is strictly verified.The formulas (10) and (11) in this paper can be used to discuss the region of motion of the general three-body problem and some explicit results will be discussed in an other article.
|
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
