Non-linear stability of the equilibria in the gravity field of a finite straight segment

Details Non-linear stability of the equilibria in the gravity field of a finite straight segment Non-linear stability of the equilibria in the gravity field of a finite straight segment

Nov 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001cemda..81..235r&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 81, Issue 3, p. 235-248 (2001).

Astronomy and Astrophysics

Astronomy

3

Normal Forms, Stability

Scientific paper

We study the non-linear stability of the equilibria corresponding to the motion of a particle orbiting around a finite straight segment. The potential is a logarithmic function and may be considered as an approximation to the one generated by elongated celestial bodies. By means of the Arnold's theorem for non-definite quadratic forms we determine the orbital stability of the equilibria, for all values of the parameter k of the problem, resonant cases included.

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