The Regular Tetrahedron Extension of Lagrange's Three Bodies

Details The Regular Tetrahedron Extension of Lagrange's Three Bodies The Regular Tetrahedron Extension of Lagrange's Three Bodies

Jul 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994mnras.269..451w&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Vol. 269, NO. 2/JUL15, P. 451, 1994

Mathematics

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Scientific paper

It is shown that four particles of any mass ratio on the vertices of a regular tetrahedron form an equilibrium configuration in expanding cosmological coordinates. This configuration is unstable to all normal modes of motion, although not violently so, and with a force law shallower than inverse first power it can become stable. Details of the instability are discussed using numerical calculations as well as group theory. Applications to galaxy formation and the dynamics of small groups of galaxies are mentioned. Key words: instabilities - celestial mechanics, stellar dynamics - galaxies: formation - cosmology: theory.

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