Rotation of synchronous satellites: application to the Galilean satellites
The equations of the \(n\)-body problem (and particularly, \( n=3 \) case) written in Keplerian variables have singularities in cases of orbits with small eccentricities and inclinations. On the contrary the Poincaré and the Laplace variables are regular for orbits with small eccentricities and inclinations, and are thus well suited for studying the planetary problem in the case of our solar system. Here, first the Laplace and the Poincaré variables are introduced, then it is demonstrated that the Poincaré action-angle variables are closely related to the geometry of the group \(\text{SO}(3)\) and the Laplace variables -- to the geometry of the group \(\text{SU}(2)\) and, finally, an algorithm easily implementable on a computer is constructed. The algorithm called POINCARE program performs series developments and averaging processes and it is written in the MAPLE algorithmic language.
scientific article; zbMATH DE number 2140052