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- W2113789531 abstract "An analysis is performed for the nonlinear motion of a particle near the equilateral points in the restricted problem of three bodies for the case fJL « /i2, i.e., cr = o?i — 2co2 ~ 0 (wi and o>2 are the frequencies of the two modes of oscillation of the linearized equations). The analysis is carried out to second order in amplitude using both the method of multiple scales and a method of averaging. It is found that the results of both methods are in full agreement. Also, it is found that long period orbits are given by [2(co 2)1/2^i — p]2 + C0i^22 = p 2 where AI and Az are the amplitudes of the two modes of oscillation and p = a sinmr/2/4C(co2)1/2, n = — 1 and 1, where C is a positive known function of the mass ratio of the two primaries. The results show that these long period orbits are stable only if A < |cr| 12Cc02. Short period orbits are found to be unstable, in the sense that if they are subjected to small disturbances the resultant motions are no longer short period orbits. At /i = /z 2, all motions near L4 are found to be unstable. The time variation of the amplitude of an aperiodic motion is presented in terms of elliptic functions." @default.
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- W2113789531 date "1970-12-01" @default.
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- W2113789531 title "Three-to-one resonances near the equilateral libration points" @default.
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- W2113789531 doi "https://doi.org/10.2514/3.6095" @default.
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