\documentstyle{article}
\title{On the rotation of a triaxial rigid body. Fourier series expansions}
\author{A. Abad, A. Elipe \\
       {\small Grupo de Mec\'anica Espacial. Universidad de Zaragoza. 
      50009 Zaragoza. Spain}\\[1.5ex]
      M. Vallejo\\
      {\small Real Observatorio de la Armada. 11110 San Fernando. C\'adiz.
      Spain  } }
\date{}

\begin{document}
\maketitle

We propose here a new approach to the rotation of a triaxial rigid body
under a
gravitational field. There is no assumption on the axes of inertia.
\par
It is well known that elliptic functions appear in the solution of the
Euler equations in the free rotation of a triaxial rigid body. Let us 
assume
that the gravitational field is a perturbation (which is true in most of 
the
celestial bodies). Our approach consists of using the solution of the
unperturbed part (that contains elliptic functions) to expand the 
perturbation
in a Fourier series, which coefficients are polynomials of the Jacobian 
nome.
These series converge very fast, and thus, with only few terms a good
approximation is obtained.
Once the expansion is obtained, it is possible to apply to it a
Lie-transformation. 
Several application to artificial and natural bodies have been carried out.
\end{document}

