Open AccessFurther consideration of the stability of the pear-shaped figure of a rotating mass of liquid
Author(s) -
George Howard Darwin
Publication year - 1908
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.1908.0012
Subject(s) - pear , stability (learning theory) , sign (mathematics) , instability , mathematics , physics , mechanics , computer science , mathematical analysis , machine learning , world wide web
In vol. 17, No. 3 (1905), of the ‘Memoirs of the Imperial Academy of St. Petersburg,' M. Liapounoff has published an abstract of his work on figures of equilibrium of rotating liquid under the title “Sur un Problème de Tchebychef.” In this paper he explains how he has obtained a rigorous solution for the figure and stability of the pear-shaped figure, and he pronounces it to be unstable. In my paper in the ‘Philosphical Transactions’ I had arrived at an opposite conclusion. The stability or instability depends, in fact, on whether the sign of a certain function, which M. Liapounoff calls A, is negative or positive.