Stability of and motion aboutL
4 at three-to-one commensurability |
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| Authors: | K T Alfriend |
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| Institution: | (1) Department of Theoretical and Applied Mechanics, Cornell University, 14850 Ithaca, New York, U.S.A. |
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| Abstract: | The stability ofL
4 and the motion aboutL
4 in the restricted problem of three bodies is investigated when there is three-to-one commensurability between the long and short periods of motion, that is, when the mass ratio  has the value =0.013516.... The two time scale method is used (1) to show thatL
4 is an unstable equilibrium point when =3, (2) to determine for what initial conditions periodic orbits occur when  3, (3) to determine the stability of the periodic orbits, and (4) to investigate the boundedness of the motions aboutL
4 when 3. |
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| Keywords: | |
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