Invited Review, to be published in
``Recent Research Developments in Astrophysics,''
by Research Signpost, India 2002

Draft version can be found in archive http://xxx.lanl.gov as
astro-ph/0208489

Complex rotation with internal dissipation. 
Applications to cosmic-dust alignment and to wobbling comets and asteroids.

M.Efroimsky, A.Lazarian, V.Sidorenko

Asteroid, cometary nucleus,  spacecraft,  as well as whatever other freely 
spinning body dissipate energy when  they  rotate  about  any  axis  different 
from principal. We discuss  the internal-dissipation-caused  relaxation  of  
a freely precessing  rotator  towards  its minimal-energy mode  (mode that 
corresponds to  the spin about the maximal-inertia axis).  We show  that this 
simple  system contains in itself  some quite unexpected physics.  While the
body nutates at some rate,  the internal stresses and strains  within the body 
oscillate at frequencies  both  higher and  (what is  especially surprising)  
lower than  this rate.  The internal  dissipation  takes place  not so much  
at the frequency  of nutation  but rather at the second and higher harmonics.
In other words, this  mechanical system provides  an example  of an  extreme 
non-linerity.  Issues  like chaos and separatrix  also come into play.  The 
earlier  estimates,  that ignored non-linearity,  considerably underestimated
the efficiency  of the internal relaxation of wobbling asteroids and  comets. 
At the same time, owing to the non-linearlity  of inelastic  relaxation,  
small-angle  nutations  can  persist for very long time  spans.  The latter 
circumstance is important  for  the analysis  and  interpretation  of NEAR's 
data on  Eros'  rotation state.  Regarding  the comets,  estimates  show  that
the currently available  angular  resolution  of  spacecraft-based instruments
makes it  possible  to  observe wobble damping  within year- or  maybe even 
month-long spans  of time. Our review also covers pertinent topics from the 
cosmic-dust  astrophysics;  in particular,  the role played by precession 
damping  in the dust alignment. We show that this damping provides coupling of
the grain's rotational and vibrational degrees of freedom; this  entails 
occasional flipping of dust grains due to thermal fluctuations.  During such a 
flip, grain preserves its angular momentum, but the  direction of torques 
arising from H$_2$ formation reverses. As a  result, flipping grain will not 
rotate fast in spite of the action of  uncompensated H$_2$ formation torques. 
The grains get ``thermally
  trapped,'' and their alignment is marginal. 
Inelastic relaxation  competes with the nuclear and Barnett relaxations, so 
we define  the range of sizes for which the inelastic relaxation dominates.