http://www.dept.aoe.vt.edu/~cdhall/courses/KlueverText/SDC.pdf

Theory of orbits. The restricted problem of three bodies

Spacecraft Dynamics and Control

This paper offers a modification of the Cowell method for the integration of orbits The modification is characterized by the property that it will integrate unperturbed Kepler motion exactly (excluding truncation errors), thus the slight instability of the Cowell Method is avoided Furthermore, the modification takes into account the most important secular effects of orbit motion As an example of the applicability of the modified method to perturbed motion, the equations of motion of an artificial earth satellite are integrated In the case of elliptic initial conditions regularization by a Levi-Civita transformation was used

Stabilization of Cowell's method

Analytical solutions for quasi-periodic orbits about the translunar libration point are obtained by using the method of Lindstedt-Poincare and computerized algebraic manipulations. The solutions include the effects of nonlinearities, lunar orbital eccentricity, and the sun's gravitational field. For a small-amplitude orbit, the orbital path as viewed from the earth traces out a Lissajous figure. This is due to a small difference in the fundamental frequencies of the in-plane and out-of-plane oscillations. However, when the amplitude of the in-plane oscillation is greater than 32,379 km, there is a corresponding value of the out-of-plane amplitude that will produce a path where the fundamental frequencies are equal. This synchronized trajectory describes a 'halo orbit' of the moon.

Quasi-periodic orbits about the translunar libration point.

methods

https://www-m3.ma.tum.de/foswiki/pub/M3/Allgemeines/JuMaOb05-DMOC/JuMaOb-DMOC-IFAC05.pdf

Theory of orbits. The restricted problem of three bodies

Citations

Spacecraft Dynamics and Control

Stabilization of Cowell's method

Quasi-periodic orbits about the translunar libration point.

Discrete mechanics and optimal control

Papers and proceedings

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