Central configurations of four bodies with one inferior mass |
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Authors: | R F Arenstorf |
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Institution: | (1) Dept. of Mathematics, Vanderbilt University, Nashville, Tennessee, USA |
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Abstract: | The number of equivalence classes of central configurations (abbr. c.c.) in the planar 4-body problem with three arbitrary and a fourth small mass is investigated. These c.c. are derived according to their generic origin in the 3-body problem. It is shown that each 3-body collinear c.c. generates exactly 2 non-collinear c.c. (besides 4 collinear ones) of 4 bodies with smallm
4 0; and that any 3-body equilateral triangle c.c. generates exactly 8 or 9 or 10 (depending onm
1,m
2,m
3) planar 4-body c.c. withm
4=0. Further, every one of these c.c. can be continued uniquely to sufficiently smallm
4>0 except when there are just 9; then exactly one of them is degenerate, and we conjecture that it is not continuable tom
4>0.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics. |
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Keywords: | |
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