Central configurations of four gravitational masses with an axis of symmetry
Identifieur interne : 001071 ( Crin/Checkpoint ); précédent : 001070; suivant : 001072Central configurations of four gravitational masses with an axis of symmetry
Auteurs : Daniel LazardSource :
English descriptors
Abstract
A central configuration of n masses under gravitational potential is a configuration such that all accelerations are oriented toward the center of masses and are 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 those of Lagrange. 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. In this case symmetric masses are equal. In the case where none of the masses are on the axis (trapezoidal configuration), it is rather easy to show that for any value of the two masses, there is exactly one central configuration.
Links toward previous steps (curation, corpus...)
Links to Exploration step
CRIN:lazard02dLe document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" wicri:score="430">Central configurations of four gravitational masses with an axis of symmetry</title></titleStmt><publicationStmt><idno type="RBID">CRIN:lazard02d</idno><date when="2002" year="2002">2002</date><idno type="wicri:Area/Crin/Corpus">003601</idno><idno type="wicri:Area/Crin/Curation">003601</idno><idno type="wicri:explorRef" wicri:stream="Crin" wicri:step="Curation">003601</idno><idno type="wicri:Area/Crin/Checkpoint">001071</idno><idno type="wicri:explorRef" wicri:stream="Crin" wicri:step="Checkpoint">001071</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Central configurations of four gravitational masses with an axis of symmetry</title><author><name sortKey="Lazard, Daniel" sort="Lazard, Daniel" uniqKey="Lazard D" first="Daniel" last="Lazard">Daniel Lazard</name></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>celestial mechanics</term><term>central configurations</term><term>polynomial system</term><term>real solutions</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en" wicri:score="3126">A central configuration of n masses under gravitational potential is a configuration such that all accelerations are oriented toward the center of masses and are 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 those of Lagrange. 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. In this case symmetric masses are equal. In the case where none of the masses are on the axis (trapezoidal configuration), it is rather easy to show that for any value of the two masses, there is exactly one central configuration.</div></front></TEI><BibTex type="inproceedings"><ref>lazard02d</ref><crinnumber>A02-R-454</crinnumber><category>6</category><equipe>SPACES</equipe><author><e>Lazard, Daniel</e></author><title>Central configurations of four gravitational masses with an axis of symmetry</title><booktitle>{8th International Conference on Applications of Computer Algebra - ACA 2002, Volos, Grèce}</booktitle><year>2002</year><month>Jun</month><url>http://www.loria.fr/publications/2002/A02-R-454/A02-R-454.ps</url><keywords><e>central configurations</e><e>celestial mechanics</e><e>polynomial system</e><e>real solutions</e></keywords><abstract>A central configuration of n masses under gravitational potential is a configuration such that all accelerations are oriented toward the center of masses and are 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 those of Lagrange. 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. In this case symmetric masses are equal. In the case where none of the masses are on the axis (trapezoidal configuration), it is rather easy to show that for any value of the two masses, there is exactly one central configuration.</abstract></BibTex></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Crin/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001071 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Crin/Checkpoint/biblio.hfd -nk 001071 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Crin
|étape= Checkpoint
|type= RBID
|clé= CRIN:lazard02d
|texte= Central configurations of four gravitational masses with an axis of symmetry
}}
| This area was generated with Dilib version V0.6.33. |  |