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arXiv · 2409.03934

Symmetric periodic solutions in the generalized Sitnikov Problem with homotopy methods

Carlos Barrera-Anzaldo·Carlos García-Azpeitia
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Abstract

The paper investigates a generalization of the classical Sitnikov problem, concentrating on the movement of a satellite along the Z-axis as it interacts with $n$ primary bodies in periodic motion. It establishes the existence of an infinite number of even and anti-periodic solutions with increasing periods. The proof employs the Leray-Schauder degree theory to trace the critical points of action functionals, using a homotopy from solutions when the primary bodies are transformed into circular orbits.

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Carlos Barrera-Anzaldo, Carlos García-Azpeitia. 2024-09-05. Symmetric periodic solutions in the generalized Sitnikov Problem with homotopy methods. https://arxiv.org/abs/2409.03934

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