Effect of Krein signatures on the stability of relative equilibria

Details Effect of Krein signatures on the stability of relative equilibria Effect of Krein signatures on the stability of relative equilibria

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995cemda..61..217c&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 61, no. 3, p. 217-238

Mathematics

1

Lagrangian Equilibrium Points, Linearity, Perturbation, Signatures, Stability, Synchronous Satellites, Three Body Problem, Eigenvalues, Matrices (Mathematics), Oblate Spheroids, Prolate Spheroids

Scientific paper

We consider the linear stability of the equilibrium points of the generic rotating potentials U(r), U(r, theta, U(r, phi ) and U(r, phi). The stability analysis is performed using the concept of Krein's signature. This signature is calculated for all eigenvalues of the above potentials. Thereby, the Lagrangian points of the restricted three-body problem and the synchronous satellites of oblate and prolate planets are also studied. We find also the new positions of the eigenvalues for perturbations of the original L4 and L5 points of Mars, Jupiter, Saturn, Uranus and Neptune. Finally, we study the problem with the mass ratio mu close to the critical value and the stability of geostationary satellites perturbed by the Moon.

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