## The Application of Floquet Theory to the Computation of Small Orbital Perturbations Over Long Time Intervals Using the Tschauner-Hempel EquationsDepartment of Aeronautics and Astronautics, Stanford University., 1965 - Artificial satellites - 70 pages This paper deals with a method of calculating the deviation of the path of an orbiting body from a nominal or reference trajectory. The form in which the solution is cast was motivated by a particular perturbation problem. Stanford University is developing a 'drag-free', or 'dragmakeup', scientific satellite which is designed to follow a purely gravitational orbit. The satellite consists actually of two satellites: an inner sphere or proof mass, and an outer concentric shell. The relative position of the shell with respect to the inner sphere is sensed with a capacitive pickoff. The position signals command an active translation control system which fires jets mounted on the outer shell so that it chases the inner sphere without ever touching it. Thus the proof mass is shielded from gas drag and solar radiation pressure and, except for very small disturbances caused by force interactions with the outer shell, it follows a purely gravitational orbit. |

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### Contents

Solution of the TschaunerHempel Equations | 6 |

Solution for Constant Periodic and AlmostPeriodic | 14 |

SampledData Solution | 21 |

Application to the Problem of Solar Radiation with Shadowing | 35 |

Application to Inertial Guidance | 41 |

Review of Floquet Theory | 50 |

Derivation of a Special Form of the Solution to | 56 |

The IMatrix | 64 |

References | 71 |