On Roto-Translatory Motion: Reductions and Radial Intermediaries

The roto-translational dynamics of an axial-symmetric rigid body is discussed in a central gravitational field. The six-degree-of-freedom Hamiltonian problem is formulated as a perturbation of the Kepler motion and torque-free rotation. A chain of canonical transformations is used to reduce the problem. First, the elimination of the nodes reduces the problem to a system of four degrees of freedom. Then, the elimination of the parallax simplifies the resulting Hamiltonian, which is shaped as a radial intermediary plus a remainder. Some features of this integrable intermediary are pointed out. The normalized first order system in closed form is also given, thus completing the solution. Finally the full reduction of the radial intermediary is constructed using the Hamilton-Jacobi equation.

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