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Short-axis-mode rotation of a free rigid body by perturbation series

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Abstract

A simple rearrangement of the torque free motion Hamiltonian shapes it as a perturbation problem for bodies rotating close to the principal axis of maximum inertia, independently of their triaxiality. The complete reduction of the main part of this Hamiltonian via the Hamilton–Jacobi equation provides the action-angle variables that ease the construction of a perturbation solution by Lie transforms. The lowest orders of the transformation equations of the perturbation solution are checked to agree with Kinoshita’s corresponding expansions for the exact solution of the free rigid body problem. For approximately axisymmetric bodies rotating close to the principal axis of maximum inertia, the common case of major solar system bodies, the new approach is advantageous over classical expansions based on a small triaxiality parameter.

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Notes

  1. Andoyer’s triaxiality coefficient \(\beta \) is noted \(e\) by Kinoshita (1972) who, besides, instead of \(\alpha \) uses the inertia parameter \(D=-C/\alpha \) first proposed by Hitzl and Breakwell (1971).

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Acknowledgments

Support is acknowledged from projects AYA 2009-11896 and AYA 2010-18796 of the Government of Spain.

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  1. Columnas de Hercules 1, 11100 , San Fernando, Spain

    Martin Lara

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  1. Martin Lara
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Lara, M. Short-axis-mode rotation of a free rigid body by perturbation series. Celest Mech Dyn Astr 118, 221–234 (2014). https://doi.org/10.1007/s10569-014-9532-0

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