Verhaar, E. (2014) On the theory of collisional orbits in the two center problem. Bachelor's Thesis, Mathematics.
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Abstract
The two center problem or Euler's three body problem, concerns motion of a mass around two fixed centers of attraction. In this paper, we will specifically look at one-parameter families of non-collisional orbits in the planar case of the two center problem. The system is integrable and hence, by the Liouville-Arnold theorem, the phase space is foliated by invariant 2-tori. To find these 2-tori we make use of elliptic coordinates. Orbits lying on a 2-torus and are either periodic or quasi-periodic. Quasi-periodic orbits will densely fill the torus, so no one-parameter families of non-collisional orbits exist. We will show that in the case of periodic orbits, there can be at most two distinct collisional orbits and there exist one-parameter families of non-collisional orbits.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 07:56 |
| Last Modified: | 15 Feb 2018 07:56 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/11581 |
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