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Zhihong Xia (1991)
Central configurations with many small massesJournal of Differential Equations, 91
A. Fernandes, B. Garcia, Jaume Llibre, Luis Mello, Antonio Carlos, Fernandes, B. Garcia, Jaume Llibre, Luis Mello (2017)
New central configurations of the (n+1)-body problemJournal of Geometry and Physics, 124
F. Moulton (1910)
The Straight Line Solutions of the Problem of N BodiesAnnals of Mathematics, 12
R. Arenstorf (1982)
Central configurations of four bodies with one inferior massCelestial mechanics, 28
A. Albouy, V. Kaloshin (2012)
Finiteness of central configurations of five bodies in the planeAnnals of Mathematics, 176
J. Barros, Eduardo Leandro (2011)
The Set of Degenerate Central Configurations in the Planar Restricted Four-Body ProblemSIAM J. Math. Anal., 43
(1970)
Celestial Mechanics: Vol. 1
J. Palmore (2007)
CLASSIFYING RELATIVE EQUILIBRIA. II
(1767)
De moto rectilineo trium corporum se mutuo attahentium
M. Alvarez-Ramírez, A. Santos, C. Vidal (2013)
On Co-Circular Central Configurations in the Four and Five Body-Problems for Homogeneous Force LawJournal of Dynamics and Differential Equations, 25
A. Albouy, Yanning Fu (2006)
Euler configurations and quasi-polynomial systemsRegular and Chaotic Dynamics, 12
(1970)
Topology and Mechanics: 2. The Planar n-Body Problem
M. Alvarez-Ramírez, J. Llibre (2019)
Equilic quadrilateral central configurationsCommun. Nonlinear Sci. Numer. Simul., 78
J. Barros, Eduardo Leandro (2014)
Bifurcations and Enumeration of Classes of Relative Equilibria in the Planar Restricted Four-Body ProblemSIAM J. Math. Anal., 46
M. Hampton, R. Moeckel (2006)
Finiteness of relative equilibria of the four-body problemInventiones mathematicae, 163
Eduardo Piña, P. Lonngi (2009)
Central configurations for the planar Newtonian four-body problemCelestial Mechanics and Dynamical Astronomy, 108
A. Albouy (1997)
Recherches sur le problème des 'n' corps., 58
(1944)
Librationspunkte im restringierten Vierkörperproblem, Danske Vid
Essai surle probléme des trois corps, recueil des pièces qui ont remporté le prix de l'Académie royale des Sciences de Paris,tome IX,1772
Y. Long, Shanzhong Sun (2002)
Four-Body Central Configurations¶with some Equal MassesArchive for Rational Mechanics and Analysis, 162
K. Meyer (1987)
Bifurcation of a central configurationCelestial mechanics, 40
J. Palmore (1973)
Classifying relative equilibria. IIILetters in Mathematical Physics, 1
D. Saari (1980)
On the role and the properties ofn body central configurationsCelestial mechanics, 21
A. Albouy, Yanning Fu, Shanzhong Sun (2007)
Symmetry of planar four-body convex central configurationsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464
Candice Davis, Scott Geyer, William Johnson, Zhifu Xie (2018)
Inverse problem of central configurations in the collinear 5-body problemJournal of Mathematical Physics, 59
W. Macmillan, W. Bartky (1932)
Permanent configurations in the problem of four bodiesTransactions of the American Mathematical Society, 34
Giulio Bisconcini (1906)
Sur le problème des trois corpsActa Mathematica, 30
Y. Long (2003)
Admissible Shapes of 4-Body Non-collinear Relative EquilibriaAdvanced Nonlinear Studies, 3
A. Albouy, A. Chenciner (1997)
Le problème des n corps et les distances mutuellesInventiones mathematicae, 131
Dziobek
Ueber einen merkwürdigen Fall des VielkörperproblemsAstronomische Nachrichten, 152
Montserrat Corbera, J. Llibre (2014)
Central configurations of the 4-body problem with masses m1 = m2 > m3 = m4 = m > 0 and m smallAppl. Math. Comput., 246
M. Josefsson (2011)
More Characterizations of Tangential Quadrilaterals
A. Albouy, V. Kaloshin (2012)
Finiteness of central congurations of ve bodies in the plane
M. Alvarez-Ramírez, J. Llibre (2019)
Hjelmslev quadrilateral central configurationsPhysics Letters A
E. Pérez-Chavela, Manuele Santoprete (2007)
Convex Four-Body Central Configurations with Some Equal MassesArchive for Rational Mechanics and Analysis, 185
M. Alvarez-Ramírez, J. Llibre (2013)
The symmetric central configurations of the 4-body problem with massesAppl. Math. Comput., 219
S. Smale (1970)
Topology and mechanics. IIInventiones mathematicae, 11
Zhihong Xia (2004)
Convex central configurations for the n-body problem☆Journal of Differential Equations, 200
R. Moeckel (2001)
Generic Finiteness for Dziobek ConfigurationsTransactions of the American Mathematical Society, 353
A. Albouy (1995)
Symétrie des configurations centrales de quatre corps, 320
A. Wintner (2014)
The Analytical Foundations of Celestial Mechanics
C. Simó (1978)
Relative equilibrium solutions in the four body problemCelestial mechanics, 18
J. Llibre (1990)
On the number of central configurations in the N-body problemCelestial Mechanics and Dynamical Astronomy, 50
Montserrat Corbera, J. Cors, J. Llibre, E. Pérez-Chavela (2017)
Trapezoid central configurationsAppl. Math. Comput., 346
A. Fernandes, J. Llibre, L. Mello (2017)
Convex Central Configurations of the 4-Body Problem with Two Pairs of Equal Adjacent MassesArchive for Rational Mechanics and Analysis, 226
J. Cors, G. Roberts (2012)
Four-body co-circular central configurationsNonlinearity, 25
J. Gannaway (1981)
Determination of all central configurations in the planar 4-body problem with one inferior mass
B. Érdi, Z. Czirják (2016)
Central configurations of four bodies with an axis of symmetryCelestial Mechanics and Dynamical Astronomy, 125
d) The value ( a, b ) = (1 , 1) ∈ Σ 3 corresponds to the tangential trapezoid given by the square with four equal masses at its vertices
Eduardo Leandro (2003)
Finiteness and Bifurcations of some Symmetrical Classes of Central ConfigurationsArchive for Rational Mechanics and Analysis, 167
R. Moeckel (1990)
On central configurationsMathematische Zeitschrift, 205
Zhifu Xie (2012)
Isosceles trapezoid central configurations of the Newtonian four-body problemProceedings of the Royal Society of Edinburgh: Section A Mathematics, 142
Jaume Llibre (1976)
Posiciones de equilibrio relativo del problema de $4$ cuerposPublicacions Matematiques, 3
A tangential trapezoid, also called a circumscribed trapezoid, is a trapezoid whose four sides are all tangent to a circle within the trapezoid: the in-circle or inscribed circle. In this paper we classify all planar four-body central configurations, where the four bodies are at the vertices of a tangential trapezoid.
Regular and Chaotic Dynamics – Springer Journals
Published: Nov 29, 2020
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