Shooting for collinear periodic orbits in the Helium model

The frozen-planet periodic orbit of the classical collinear Helium model with negative energy is shown to exist by a simple shooting argument. This simplifies the approach established in Cieliebak et al. (Ann Inst H Poincaré Anal Non Linéaire 40:379–455, 2022). With this argument, it also follows th...

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Veröffentlicht in:	Zeitschrift für angewandte Mathematik und Physik 2023-12, Vol.74 (6), Article 227
1. Verfasser:	Zhao, Lei
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Schlagworte:	Engineering Helium Mathematical Methods in Physics Planetary orbits Theoretical and Applied Mechanics
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description	The frozen-planet periodic orbit of the classical collinear Helium model with negative energy is shown to exist by a simple shooting argument. This simplifies the approach established in Cieliebak et al. (Ann Inst H Poincaré Anal Non Linéaire 40:379–455, 2022). With this argument, it also follows that the algebraic count of the number of such orbits with a given negative energy is 1, as recently established in Cieliebak et al. (Nondegeneracy and integral count of frozen-planet orbits in helium, 2022. arXiv:2209.12634 ). The same argument also leads to the existence of other collinear periodic orbits of the classical collinear Helium model.
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title	Shooting for collinear periodic orbits in the Helium model
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