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Study of the Case with Only Two Degrees of Freedom

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Part of the Astrophysics and Space Science Library book series (ASSL,volume 443)

Abstract

We will limit ourselves to the simplest case which is the one where there are only two degrees of freedom ; I do not need to concern myself in fact with the case where there is only one degree of freedom because the equations of dynamics then are easily and simply integrated.

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Fig. 1
Fig. 2

Notes

  1. 1.

    The reason why I'm writing this last relationship can easily be seen: the arc BC is entirely above the X-axis, as can be seen in the figure, which leads to the inequality \( x_{2} > 0 \); it is clear that this inequality will still be satisfied for sufficiently small values of \( \mu \).

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Correspondence to Henri Poincaré .

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Poincaré, H. (2017). Study of the Case with Only Two Degrees of Freedom. In: The Three-Body Problem and the Equations of Dynamics. Astrophysics and Space Science Library, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-52899-1_4

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