On the Number of Unstable Modes of an Equilibrium - Part Two

Details On the Number of Unstable Modes of an Equilibrium - Part Two On the Number of Unstable Modes of an Equilibrium - Part Two

Dec 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979mnras.189..817k&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Vol. 189, P. 817, 1979

Mathematics

Logic

27

Scientific paper

For stable equilibria associated with maxima or minima 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.

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