A study of the secular deceleration of the earth's rotation using a hamiltonian formalism

In this article, the secular rotational varitation of the Earth whose elastic mantle is deformed by gravitational attraction of the Moon and the Sun is studied by means of a Hamiltonian method. The expression of the tidal potential with phase lag is given. The value of the secular deceleration of the Earth's rotation is obtained for the Earth model PREM. it theoretically is -5.7 x 10(-22) rad/s(2), which agrees perfectly with the latest observational results. The results also show that the principle contribution to this deceleration is the sectorial tide corresponding to the term m = 2, and that the deformation produced by the Moon is much more important than that due to the Sun.