"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)
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
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)