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Central Configurations of Four Gravitational Masses with an Axys of Symmetry

Daniel Lazard 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This talk describes a common work with J.-C. Faugère. A central configuration of n masses under gravitational potential is a configuration such all accelerations are oriented toward the center of masses and proportional to the distance to this center. It follows that the plane central configurations are those that remain homothetic to themselves, with convenient initial velocities. For three masses, these configurations are well known as Lagrange positions. A well known conjecture is that the number of central configurations of n bodies is always finite when the masses are fixed. In this talk, we describe the number of central configurations of four masses in the plane, which have an axis of symmetry such symmetric masses are equal.
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Submitted on : Thursday, October 19, 2006 - 9:03:10 AM
Last modification on : Friday, February 26, 2021 - 3:28:06 PM
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  • HAL Id : inria-00107620, version 1



Daniel Lazard. Central Configurations of Four Gravitational Masses with an Axys of Symmetry. Workshop on Applications of Commutative Algebra - Catania 2002, 2002, Catania, Italie. ⟨inria-00107620⟩



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