The meromorphic non-integrability of the planar three-body problem
Alexei Tsygvintsev
TL;DR
This paper proves that the planar three-body problem does not admit a complete set of complex meromorphic first integrals near the Lagrangian solution, indicating its non-integrability.
Contribution
It establishes the non-integrability of the planar three-body problem in the complex meromorphic sense near the Lagrangian solution.
Findings
No complete set of complex meromorphic first integrals exists near the Lagrangian solution.
The three-body problem exhibits non-integrability in the complex meromorphic framework.
Abstract
We study the planar three-body problem and prove the absence of a complete set of complex meromorphic first integrals in a neighborhood of the Lagrangian solution.
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Taxonomy
TopicsSpacecraft Dynamics and Control