Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974afz....10..585n&link_type=abstract
Astrofizika, vol. 10, Nov. 1974, p. 585-592. In Russian.
Astronomy and Astrophysics
Astrophysics
Astronomical Models, Dynamic Stability, Explosions, Galactic Nuclei, Gravitational Effects, Astrophysics, Condensing, Modal Response, Variational Principles
Scientific paper
Unstable frequency modes prior to collision and after explosion are calculated for central shell configurations (self-gravitating systems formed by a continuous layer of condensed matter) with axisymmetric perturbations. A configuration with axisymmetric motion is defined mathematically, and an instability is demonstrated. A system of equations defining the behavior of the configuration is derived, including various equations of motion, equation for a discontinuity on the surface of the sphere, and equations relating the internal and external normal and tangential (to the meridian) derivatives of the potential of a simple layer. All the unstable frequency modes are calculated, and it is shown that such configurations are unstable both before collision and after explosion.
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