Generic Finiteness for Dziobek Configurations

Moeckel, Richard

doi:10.1090/s0002-9947-01-02828-8

Cited by 42 publications

(33 citation statements)

References 12 publications

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“…It was also published in Moeckel (2001 as an easy consequence of (2.4). But (2.4) is not an obvious corollary of (3.1), and none of these four authors wrote it.…”

Section: Routh Versus Dziobekmentioning

confidence: 94%

“…Dziobek and many authors after him chose to skip it. An elegant and complete presentation is given in Moeckel (2001).…”

Section: Routh Versus Dziobekmentioning

confidence: 99%

“…The non-planar case seems easier because Dziobek's coordinates are available. Using them, Moeckel (2001) succeeded in proving the finiteness for almost any choice of masses. But still we do not know, for example, the answer in the case m 1 Zm 2 Zm 3 Zm 4 Zm 5 .…”

Section: The Main Lemmasmentioning

confidence: 99%

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Symmetry of planar four-body convex central configurations

Albouy

Sun

2008

Proc. R. Soc. A.

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We study the relationship between the masses and the geometric properties of central configurations. We prove that, in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.

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“…It was also published in Moeckel (2001 as an easy consequence of (2.4). But (2.4) is not an obvious corollary of (3.1), and none of these four authors wrote it.…”

Section: Routh Versus Dziobekmentioning

confidence: 94%

“…Dziobek and many authors after him chose to skip it. An elegant and complete presentation is given in Moeckel (2001).…”

Section: Routh Versus Dziobekmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry of planar four-body convex central configurations

Albouy

Sun

2008

Proc. R. Soc. A.

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“…For the spatial 5-body problem Moeckel in Moeckel (2001) established the generic finiteness of Dziobek's CCs (CCs which are non-planar). A computer-assisted work by Hampton and Jensen (2011) strengthens this result by giving an explicit list of conditions for exceptional values of masses.…”

Section: State Of the Artmentioning

confidence: 99%

Central configurations in the spatial n-body problem for $$n=5,6$$ with equal masses

Moczurad

Zgliczyński

2020

Celest Mech Dyn Astr

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We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for $$n=5$$ n = 5 and 6, with equal masses. For each central configuration, we give a full list of its Euclidean symmetries. For all masses sufficiently close to the equal masses case, we give an exact count of configurations in the planar case for $$n=4,5,6,7$$ n = 4 , 5 , 6 , 7 and in the spatial case for $$n=4,5,6$$ n = 4 , 5 , 6 .

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“…Another result valid for any number of bodies, due to Richard Moeckel, is a generic finiteness result for N bodies in R N −1 [20].…”

Section: Marshall Hampton and Anders Nedergaard Jensenmentioning

confidence: 99%