The Control and Use of Drag-Free Satellites

by Benjamin Lange, June 1964

Acknowledgement

Originally in 1999 the pages of this thesis were scanned and put on the Odie website by Allison Floyd of the Stanford University Space Systems Development Laboratory. The Odie project now no longer exists, and its website has been removed. The director of the laboratory, Professor Bob Twiggs, however, has furnished me with the scanned pages of the thesis.

Title Page, Acknowledgements, Abstract, Table of Contents, Notation, Pages i - xxxiv

Introduction, Pages 1 - 8

Chapter 1: Derivation of the Dynamical Equations, Pages 9 - 38

Chapter 2: Translation Control with Perfect 3-Axis Attitude Control, Pages 39 - 69

Chapter 3: Translation Control With Partial or No Attitude Control With Applications to the Control of Spinning Vehicles and Other Dynamically Similar Plants, Pages 70 - 108

Chapter 4: System Trajectory Errors, Pages 109 - 144

Chapter 5: The Unsupported Gyroscope, Pages 145 - 169

Conclusion and References, Pages 170 - 174

From a modern (2003) point of view, there are three expositions in this thesis which are still interesting:

1. The derivation of the effects of magnetic eddy currents in a spinning conducting sphere in Chapter 5, pp. 153 - 160.
2. The discussion of the solutions of the linear orbit equations of relative translation (Euler-Hill equations) in Chapter 4, pp. 110 - 125.
3. The discussion of the attitude control of spinning symmetric satellites using Frequency Symmetry, Chapter 3, pp. 72 - 97.

The treatments of the translation disturbances in the thesis do not include power spectral densities which are part of the LISA drag-free requirement. For the LISA disturbance PSD's, see the two papers Errors of a Spherical Proof Mass in LISA and SPIE 2002 Telescope Conference: Spherical Proof Masses in LISA both linked on this website.

The Unsupported Gyro drifts are treated much more thoroughly in the Relativity Gyro paper also linked on this website.