The number of planar central configurations for the $4$–body problem is finite when $3$ mass positions are fixed
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- by Martha Alvarez, Montserrat Corbera, Joaquin Delgado and Jaume Llibre PDF
- Proc. Amer. Math. Soc. 133 (2005), 529-536 Request permission
Abstract:
In the $n$–body problem a central configuration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for $n=3$ and for $n>4$ that if $n-1$ masses are located at fixed points in the plane, then there are only a finite number of ways to position the remaining $n$th mass in such a way that they define a central configuration. Lindstrom leaves open the case $n=4$. In this paper we prove the case $n=4$ using as variables the mutual distances between the particles.References
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Additional Information
- Martha Alvarez
- Affiliation: Departamento de Matemáticas, UAM–Iztapalapa, A.P. 55–534, 09340 Iztapalapa, Mexico, D.F., Mexico
- Email: mar@xanum.uam.mx
- Montserrat Corbera
- Affiliation: Departament d’Informàtica i Matemàtiques, Universitat de Vic, 08500 Vic, Barcelona, Spain
- Email: montserrat.corbera@uvic.es
- Joaquin Delgado
- Affiliation: Departamento de Matemáticas, UAM–Iztapalapa, A.P. 55–534, 09340 Iztapalapa, Mexico, D.F., Mexico
- Email: jdf@xanum.uam.mx
- Jaume Llibre
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
- Email: jllibre@mat.uab.es
- Received by editor(s): November 12, 2002
- Received by editor(s) in revised form: February 6, 2003, and July 16, 2003
- Published electronically: August 26, 2004
- Communicated by: Carmen C. Chicone
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 529-536
- MSC (2000): Primary 70F07; Secondary 70F15
- DOI: https://doi.org/10.1090/S0002-9939-04-07590-2
- MathSciNet review: 2093077