"GALILEO GALILEI" GG Space Project

Research Papers Available Online

• The  radiometer  effect  in  space   missions  to  test  the  Equivalence  Principle (November 2000)
• Evaluation of a Proposed Test of the Weak Equivalence Principle Using Earth Orbiting Bodies in High-Speed Co-Rotation: Re-Establishing the Physical Bases (Classical and Quantum Gravity, 1999)
• "Galileo Galilei" (GG). Proposed Space Experiment  to Test the equivalence Principle and Preliminary Results from the Prototype on the Ground (in Proceedings of "1999NASA/JPL International Conference on Fundamental Physics in Space", April
  29, 30 and May 1, Washington DC1999)
• The "Galileo Galilei" (GG) Project: Testing the Equivalence Principle in Space and on Earth (Advances in Space Research, 2000)
• Proposed noncryogenic, nondrag-free test of the equivalence principle in space (New Astronomy, 1998)
• Addendum No.1 to the GG PRE PHASE A REPORT: Active Control Of Whirl Motions (May 1997)

This work reports the results obtained by simulating numerically the whirl motions of two coupled rotors and their stabilization with rotating sensors/actuators. Various types of control laws are tested. It is found that the system can be stabilized with control forces of the size predicted theoretically only if appropriate control laws are designed; the control laws must take into account that the system is spinning rapidly while the whirl motions grow slowly. In essence, one should subtract away from the sensors/actuators their rapid rotation velocity by appropriate averaging and best-fitting, so as to recover the slow relative velocity of the whirl motions which needs to be damped. To the contrary, conventional control laws, in which relative velocities are computed simply from the difference of successive displacements, are not adequate unless control forces about a million times larger than necessary are applied. The need for huge control forces in this case derives from the fact that the slow relative velocity that should be damped is overcome by the far larger rotation velocity of the sensors/actuators; the actuators "fire" without knowing what to, and the final result is a system dominated by the active control forces themselves. The results obtained with conventional control laws are shown in Figure. A-2; the results obtained with the control law which is best in subtracting away the spin are shown in Figure B3-2. The difference is self apparent, and quite striking. This work has been carried out using the numerical code DCAP which has been developed by ALENIA SPAZIO under ESA contract.

• Opinion Expressed by Stephen H Crandall (MIT) on GG (May 1997)

Professor Crandall has been asked to evaluate the GG proposed experiment on the specific issue of the stabilization of whirl motions. After several months of discussions with both the GG proposing scientists and the GG reviewers at ESA, he has addressed this letter to the Chairman of the ESA panel (Maurice Jacob) and to the Principal Investigator of the GG Project (Anna M. Nobili)

• GG: Dissipation by the Electrostatic Dampers (February 1997)

Unstable whirl motions in the GG experiment are damped actively using small rotating electrostatic sensors/actuators. This work gives an estimate of the losses due to the dampers and concludes that these are negligible compared to losses in the mechanical suspensions.

• GG: Energy Gained by Whirling Motion as Fraction of Energy Lost by Spinning Rotor (February 1997)

A supercritical rotor is known to develop unstable whirl motions; see paper III above. This work disproofs the superficial idea that a faster rotor should be more unstable and gives an interesting analog in the case of celestial bodies where the amplitude of the relative motion increases because of tidal friction. Indeed, one should be very careful in applying everyday experience to supercritical rotors.

• On the Stabilization of the GG System (January1997)

Stephen H. Crandall, from MIT, is an internationally recognized expert on dissipation in rotating dynamical systems. He has accepted to review the problem of the stabilization of the GG bodies. This short note by S.H. Crandall, in collaboration with A.M. Nobili, summarizes the main aspects of the problem and provides some guidelines for the development of adequate control laws.

• Passive Vibration Isolation in a Spinning Spacecraft (November 1996)

This work gives the transfer function of a passive mechanical suspension inside a spinning spacecraft. The transfer function is computed both in the fixed frame and in the frame rotating with the spacecraft. No matter which reference frame is chosen, the weak mechanical suspension -possible in space thanks to weightlessness- ensures good attenuation of effects which act at the spin frequency in the inertial frame, i.e. of effects which, in the frame of the spacecraft, have zero frequency or twice its spin frequency.

• GG-Test of the Equivalence Principle with a Small Spinning Satellite: The Stabilization of its Weakly Coupled Masses (in Scientific Satellites Achievements and Prospects in Europe, Proceedings, AAAF-ESA, 3-74/89, 1996).
• Stabilization of Weakly Coupled Rotors: a General Derivation of the Required Forces (November 1996)

Starting from general physical principles and conservation laws, this paper derives the forces required for the stabilization of whirling motions. These forces can be applied also in the rotating frame and turn out to be a factor of 1 million weaker than the control forces used in the simulation of the GG system at ESTEC.

• Proposed new test of the Equivalence Principle in space (1995)

by A.M. Nobili, D. Bramanti, E. Polacco, G. Catastini, G. Genta, E. Brusa, V.P. Mitrofanov, A. Beranrd, P. Touboul, A.J. Cook, J. Hough, I.W. Roxburgh, A. Polnarev, W. Flury, F. Bralier, C. Marchal, Pisa preprints on Astrohyisics and Space Mechanics
(Text to download in  postscript format, 2.2 MB:  preprint.ps. Figure 8 in JPG format, 299 KB, click to view and download:  fig8.jpg)

 

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GG Project Homepage
(Anna Nobili- nobili@dm.unipi.it)
Last  edited, 01 March 2001