Open AccessNote on the stability of Jacobi's ellipsoid
Publication year - 1909
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1909.0026
Subject(s) - ellipsoid , eccentricity (behavior) , stability (learning theory) , series (stratigraphy) , mathematics , bifurcation , mathematical analysis , value (mathematics) , physics , computer science , geology , statistics , nonlinear system , paleontology , astronomy , machine learning , quantum mechanics , political science , law
It is known that Maclaurin’s spheroid of rotating liquid becomes unstable when its eccentricity reaches the value sin 54° 21' 27''. This is a form of bifurcation, and for increasing momentum the stability passes over to Jacobi’s ellipsoid. It is possible to prove these results by the method applied by me to the discussion of the stability of the pear-shaped figure of equilibrium, and it is worth while to do so, because we obtain thereby a verification of the complicated analysis used in the previous investigation, and because the series which arise are exactly similar to the former series. In vol. 3 of my ‘Scientific Papers’ I shall give a few details about the present analysis. It will here suffice to say that it gives the known results correctly, and a good approximation to the form of Jacobi’s ellipsoid.