On the number of unstable modes of an equilibrium - II
Open Access
- 1 December 1979
- journal article
- research article
- Published by Oxford University Press (OUP) in Monthly Notices of the Royal Astronomical Society
- Vol. 189 (4) , 817-822
- https://doi.org/10.1093/mnras/189.4.817
Abstract
For stable equilibria associated with maxima or mm1ma of potential functions, the number of unstable modes of each equilibrium may be deduced, in most cases of astrophysical interest, from topological properties of continuous series of equilibria, provided stability conditions are known for one configuration. No eigenvalue equation has then to be solved. Secular stability conditions for MacLaurin and Jacobi ellipsoids are rederived in this way as an illustration.Keywords
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