The Existence of Retrograde Orbits for the Four-Body Problem with Various Choices of Masses

Chong Li

doi:10.4028/www.scientific.net/AMR.871.101

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 871The Existence of Retrograde Orbits for the...

The Existence of Retrograde Orbits for the Four-Body Problem with Various Choices of Masses

Abstract:

In this paper, we study the planar Newtonian four-body problem with various choices of masses. We prove that there exist infinitely many periodic and quasi-periodic orbits with certain topological type, called retrograde orbits, that minimize the action functional on certain path spaces. On these orbits, two particles revolve around each other in one direction, while the other two particles travel on themselves orbits in opposite direction, respectively. Our proof is based on variational methods inspired by the work of Kuo-Chang Chen.

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Periodical:

Advanced Materials Research (Volume 871)

Pages:

101-106

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.871.101

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Online since:

December 2013

Authors:

Chong Li*

Keywords:

Four-Body Problem, Retrograde Orbits, Variational Methods

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References

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