Canonical approach to the free nutations of a three-layer Earth model

The Hamiltonian formalism is applied to a three-layer Earth model composed of a rigid mantle, a fluid outer core and a rigid inner core, with no dissi pation of frictional or electromagnetic origin. Analytical expressions for the free nutations are derived in a set of nonsingular canonical variables that allow a much simpler mathematical treatment. They are checked versus n umerical solutions and compared with previous results by Mathews et al. [19 91a] and Getino and Ferrandiz [1996, 1998a] with complete agreement; up to the first order in the elliptieities.