A rigorous Hamiltonian approach to the rotation of elastic bodies

Details A rigorous Hamiltonian approach to the rotation of elastic bodies A rigorous Hamiltonian approach to the rotation of elastic bodies

Mar 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..58..277g&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, vol. 58, no. 3, p. 277-295

Astronomy and Astrophysics

Astronomy

8

Centrifugal Force, Earth Rotation, Elastic Bodies, Geodynamics, Hamiltonian Functions, Nutation, Perturbation, Rotating Bodies, Canonical Forms, Kinetic Energy, Potential Energy

Scientific paper

When the problem of the rotation of a non-rigid body is studied, the usual procedure consists of adding perturbations to the Hamiltonian of the rigid solid. In some cases, as occurs with the centrifugal deformation, the new perturbations contains potentials which depend on the velocity, but usually one alter neither the definition of the canonical variables nor the method for obtaining the Hamiltonian. Although this procedure gives good estimates and its formulation is simpler, it is incorrect from a theoretical point of view. In this paper we rigorously develop a Hamiltonian formulation of the problem, considering potentials that depend on the velocity. Thus the differences between the two procedures are clearly shown, giving special emphasis to the case of the elastic Earth, for which we show that the differences obtained cannot be ignored within the accuracy limits at present required.

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