Stationary
rotations of two connected axisymmetric rigid bodies Anna D.Guerman A system of
two connected bodies (a satellite and a thin uniform rod with torsion spring
and viscous damper in the junction) that can simulate a damper device for
nutational oscillations of a spin-stabilized satellite is examined. Stationary
rotations of the system are studied for two suspension schemes. In the first
one [1] the junction is situated on the symmetry axis of the satellite, and the
spring is not deformed when the rod is aligned with this axis. In the second
scheme [2], the nominal position of the rod is orthogonal to the symmetry axis
of the satellite, and the junction is displaced from this axis. The principal
question in study is the existence of possible stationary rotations in both
cases. The conditions when such rotations exist, as well as the bifurcation
points where corresponding motions appear, are determined. A number of rotations
that exist only for some specific values of the system parameters (for example,
in the absence of the spring, or for a spherically symmetric satellite) are
also determined. The results obtained can be used
for two purposes. On the one hand, they permit one to choose the parameters of
the nutational damper to avoid undesirable motions. On the other hand, the
non-trivial rotations may be chosen as a nominal operating mode of the system.
In this case, it is possible to determine the system parameters that correspond
to the desirable angle between the symmetry axis of the satellite and its
angular momentum vector. 1.
T. R. Kane, D. A. Levinson, "A Passive
Method for Eliminating Coning of Force-Free, Axisymmetric Rigid Bodies," J. of Astronautical Sciences, 1992, Vol. 40, No. 4, 439-447. 2. S. A. Mirer, V. A.
Sarychev, "Optimal Parameters of a Spin-Stabilized Satellite with a
Pendulum-Like Damper," Cosmic Research, 1997, Vol. 35,
No. 6, 651-658. |
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