Complex instability around the rotation axis of stellar systems. II - Rotating oscillators

Details Complex instability around the rotation axis of stellar systems. II - Rotating oscillators Complex instability around the rotation axis of stellar systems. II - Rotating oscillators

Jun 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987a%26a...180...79p&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 180, no. 1-2, June 1987, p. 79-93. Research supported by the Universite de Gen

Statistics

Computation

14

Complex Systems, Computational Astrophysics, Galactic Rotation, Harmonic Oscillators, Stellar Orbits, Stellar Systems, Astronomical Models, Celestial Mechanics, Resonance

Scientific paper

The linearization of the motion around periodic orbits following the rotation axis of galaxies leads to the investigation of the behaviour of a pair of uniformly rotating harmonic oscillators, excited periodically by various frequency shifts. A 4D mapping of the motion can then be derived. The parametric resonances of a such system are then investigated, and expressions for the instability strips are found. Beside the classical Mathieu's instability strips, additional strips of complex instability occur naturally. Some simple cases are then computed numerically in order to obtain the relative typical importance of each instability strip. Spherical homogeneous galaxies have marginally unstable radial orbits, which become unstable in inhomogeneous galaxies. Flat galaxies close to axisymmetry have stable small amplitude z-axis orbits, and complex unstable large amplitude ones. Furthermore triaxial rotating galaxies display rotation dependent Mathieu's resonances.

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