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J. Math. Phys. 41, 1854 (2000); http://dx.doi.org/10.1063/1.533216 (35 pages)

# Precession of a freely rotating rigid body. Inelastic relaxation in the vicinity of poles

Michael Efroimsky

Department of Physics, Harvard University, Cambridge, Massachusetts 02138

(Received 19 July 1999; accepted 6 December 1999)

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When a solid body is freely rotating at an angular velocity Ω, the ellipsoid of constant angular momentum, in the space Ω123, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from principal. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behavior, because an infinitesimally small deviation of the body’s shape from a rotational symmetry (i.e., a small difference between the largest and second largest moments of inertia) yields libration: the precession trajectory is not a circle but an ellipse. In this article we show that often the most effective internal dissipation takes place at twice the frequency of the body’s precession. Applications to precessing asteroids, cosmic-dust alignment, and rotating satellites are discussed. © 2000 American Institute of Physics.

© 2000 American Institute of Physics

## ERRATUM

1. Erratum: "Precession of a freely rotating rigid body. Inelastic relaxation in the vicinity of poles" [J. Math. Phys. 41, 1854 (2000)]
Michael Efroimsky
J. Math. Phys. 41, 5870 (2000)JMAPAQ000041000008005870000001

## KEYWORDS and PACS

### PACS

• General theory of classical mechanics of discrete systems

• Dust processes (condensation, evaporation, sputtering, mantle growth, etc.)

• Late stages of stellar evolution (including black holes)

• Asteroids, meteoroids

• Celestial mechanics

• Celestial mechanics (including n-body problems)

## PUBLICATION DATA

### ISSN

0022-2488 (print)
1089-7658 (online)