Abstract
This paper gives an analytic existence proof of the Schubart periodic orbit with arbitrary masses, a periodic orbit with singularities in the collinear three-body problem. A “turning point” technique is introduced to exclude the possibility of extra collisions and the existence of this orbit follows by a continuity argument on differential equations generated by the regularized Hamiltonian.
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Yan, D. A simple existence proof of Schubart periodic orbit with arbitrary masses. Front. Math. China 7, 145–160 (2012). https://doi.org/10.1007/s11464-012-0171-z
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DOI: https://doi.org/10.1007/s11464-012-0171-z
Keywords
- Celestial mechanics
- Schubart periodic orbit
- three-body problem
- binary collision
- periodic solution with singularity
- regularization