zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On central configurations. (English) Zbl 0684.70005
This paper concerns central configurations of the Newtonian N-body problem. Some previously known results about central configurations are described as background material. Then, new work concerning possible shapes of central configurations, existence of spatial configurations and bifurcation of spatial configurations from planar one is presented.
Reviewer: R.Moeckel

MSC:
70F10n-body problems
70F99Dynamics of a system of particles
References:
[1]Euler, L.: De moto rectilineo trium corporum se mutuo attahentium. Novi Comm. Acad. Sci. Imp. Petrop.11, 144–151 (1967)
[2]Hall, G.R.: Central configurations of the 1+N body problem (preprint)
[3]Lagrange, J.L.: Ouvres, vol. 6, Paris, pp 272–292, 1873
[4]Moeckel, R.: Relative equilibria of the four-body problem. Ergodic Theory Dyn. Syst.5, 417–435 (1985) · Zbl 0554.14004 · doi:10.1017/S0143385700003047
[5]McGehee, R.: Singularities in classical celestial mechanics. In: Proc. of Int. Cong. Math., Helsinki, pp. 827–834, 1978
[6]Meyer, K., Schmidt, D.: Bifurcation of relative equilibria in theN-body and Kirchoff problem (preprint)
[7]Moulton, F.R.: The straight line solutions of the problem ofN bodies. Ann. Math., II. Ser12, 1–17 (1910) · doi:10.2307/2007159
[8]Pacella, F.: Central configurations and the equivariant Morse theory. Arch. Ration. Mech. Anal.97, 59–74 (1987) · Zbl 0627.58013 · doi:10.1007/BF00279846
[9]Palmore, J.: Classifying relative equilibria. I, Bull. Am. Math. Soc.79, 904–908 (1973); II, Bull. Am. Math. Soc.81, 489–491 (1975); III, Lett. Math. Phys.1, 71–73 (1975) · Zbl 0273.57016 · doi:10.1090/S0002-9904-1973-13254-9
[10]Saari, D.: On the role and properties of central configurations. Cel. Mech.21, 9–20 (1980) · Zbl 0422.70014 · doi:10.1007/BF01230241
[11]Siegel, C., Moser, J.: Lectures on celestial mechanics. Berlin, Heidelberg, New York: Springer, 1971
[12]Smale, S.: Topology and mechanics. I, Invent. Math.10, 305–331 (1970); II, Invent. Math.11, 45–64 (1970) · Zbl 0202.23201 · doi:10.1007/BF01418778
[13]Xia, S.: Central configurations with many small masses (preprint)