Out-of-Plane Motion about Libration Points: Non-Linearity and Eccentricity Effects

Details Out-of-Plane Motion about Libration Points: Non-Linearity and Eccentricity Effects Out-of-Plane Motion about Libration Points: Non-Linearity and Eccentricity Effects

Feb 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973cemec...7..177h&link_type=abstract

Celestial Mechanics, Volume 7, Issue 2, pp.177-194

Mathematics

1

Scientific paper

Out-of-plane motion about libration points is studied within the framework of the elliptic restricted three-body problem. Nonlinear motion in the circular restricted problem is given to third order in the out-of-plane amplitudeA z by Jacobi elliptic functions. Linear motion in the elliptic problem is studied using Mathieu's and Hill's equations. Additional terms needed for a complete third-order theory are found using Lindsted's method. This theory is constructed for the case of collinear libration points; for the case of triangular points, a third-order nonlinear solution is given separately in terms of Jacobi elliptic functions.

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