Bounded orbits for three bodies in ℝ4 - Archive ouverte HAL
Article Dans Une Revue Journal of Geometric Mechanics Année : 2024

Bounded orbits for three bodies in ℝ4

Holger Dullin

Résumé

We consider the Newtonian 3-body problem in dimension 4, and fix a value of the angular momentum which is compatible with this dimension. We show that the energy function cannot tend to its infimum on an unbounded sequence of states. Consequently the infimum of the energy is its minimum. This completes our previous work [A. Albouy and H. R. Dullin, Relative equilibria of the 3-body problem in [Formula: see text], J. Geom. Mech. 12(3) (2020) 323–341] on the existence of Lyapunov stable relative periodic orbits in the 3-body problem in [Formula: see text].

Dates et versions

hal-04750453 , version 1 (23-10-2024)

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Alain Albouy, Holger Dullin. Bounded orbits for three bodies in ℝ4. Journal of Geometric Mechanics, 2024, 01 (01), ⟨10.1142/S2972458924500035⟩. ⟨hal-04750453⟩
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