## Stability of a gravity gradient satellite in an elliptic orbit |

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### Contents

THE TWO VARIABLE EXPANSION PROCEDURE | 6 |

EQUATIONS OF MOTION | 9 |

PERTURBATION SCHEME | 16 |

2 other sections not shown

### Common terms and phrases

1+ecosf 6uioduopr analytical angular velocity appropriate values Assuming a solution automatically satisfied becomes C3coss2 C4sins2 characteristic equation circular orbit coefficients equal constant Cornell University coss coupled ordinary linear DeBra earth observation eliminated elliptic orbit Equating to zero equations of motion Euler Angles expression Frequency Curve gives coordinate system givesi governing condition gravitational constant gravity torques in-plane equation in-plane motion independent variable inertial parameters insure a uniformly Kane Kevorkian less than zero linear differential equations mass center moon natural frequencies Operating on 5.1 orbit eccentricity orbit plane order equations order terms ordinary differential equation ordinary linear differential out-of-plane motion partial differential equation Perturbation Pitch Axis power series problem resonance condition resonance curve resonance terms rotation secular producing terms shown in Figure sin9 slowly varying solved Stable Regions Substituting technique teth true anomaly uniformly valid solution variable expansion procedure varying time variable