Zero frequency modes of the Maclaurin spheroids

Details Zero frequency modes of the Maclaurin spheroids Zero frequency modes of the Maclaurin spheroids

May 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986rspsa.405...65b&link_type=abstract

Royal Society (London), Proceedings, Series A - Mathematical and Physical Sciences (ISSN 0080-4630), vol. 405, no. 1828, May 8,

Physics

4

Dynamic Stability, Gravitational Waves, Maclaurin Series, Newtonian Fluids, Rotating Fluids, Spheroids, Angular Velocity, Cartesian Coordinates, Continuity Equation, Legendre Functions, Stellar Rotation, Vibration Mode

Scientific paper

The location of all zero-frequency modes of oscillation along the Maclaurin sequence are found for modes corresponding to oblate spheroidal harmonics with indices (l,m) where l less than 6 (equivalently, for modes described by Lagrangian displacements whose components in Cartesian coordinates are polynomials of degree less than or equal to 5). These points of zero frequency mark the onset of instability in each mode in the context of general relativity, or when a gravitational radiation reaction term is adjointed to the Newtonian theory.

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