Winter, Elwin (2026) N-body Choreographies. Bachelor's Thesis, Physics.
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Abstract
The planar three-body problem is one of the fundamental problems of celestial mechanics, exhibiting rich dynamical behavior despite its simple formulation. Among its most re- markable solutions is the figure-eight choreography, a periodic orbit in which three equal masses follow the same figure-eight-shaped curve, equally separated in time. This thesis presents a self-contained exposition of the Chenciner–Montgomery exis- tence proof of the figure-eight solution. Beginning with the planar three-body problem for three equal masses, the equations of motion are reformulated as a variational prob- lem using Hamilton’s principle. After introducing the variational methods required for the proof, the argument is developed through a sequence of geometric and variational techniques, including symmetry reduction to the shape sphere, the exclusion of collisions for action-minimizing trajectories, and the reconstruction of the figure-eight choreography from the reduced dynamics.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Waalkens, H. and Roest, D. |
| Degree programme: | Physics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 09 Jul 2026 12:53 |
| Last Modified: | 09 Jul 2026 12:53 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37412 |
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