Abstract
IT has been known since the time of Lagrange‘s "Mècanique Analytique" (1788) that a rigid body smoothly pivoted at one of its points O and symmetrical about an axis passing through O can have steady motions of precession in which the axis of symmetry rotates uniformly about the vertical while the solid itself rotates uniformly about the axis of symmetry ; but it has been generally supposed that there is no corresponding result if the body is unsymmetrical. However, G. Grioli (Annali di Mathematica, 26, 1 ; 1947, and Rendiconti dell' Accademia Nazionale dei Lincei, 4, 420 ; 1948) has shown that under certain conditions we can have steady precession of an unsymmetrical body about a non-vertical axis. If G is the centre of mass, it is necessary that OG should be perpendicular to one of the two circular sections of the momental ellipsoid at G, and that the axis of precession should be inclined to the vertical at a definite angle which can be calculated from the same momental ellipsoid. If these conditions are satisfied, there is a doubly infinite set of motions in which OG is perpendicular to the axis of precession, and the solid rotates uniformly about OG in the same time as OG rotates uniformly about the non-vertical axis of precession.
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Precession of an Unsymmetrical Top. Nature 162, 365 (1948). https://doi.org/10.1038/162365c0
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DOI: https://doi.org/10.1038/162365c0