Dynamical coupling of periodic systems. II - A particular case of homographic solution

Details Dynamical coupling of periodic systems. II - A particular case of homographic solution Dynamical coupling of periodic systems. II - A particular case of homographic solution

Dec 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979a%26a....80..301s&link_type=abstract

Astronomy and Astrophysics, vol. 80, no. 3, Dec. 1979, p. 301-307.

Astronomy and Astrophysics

Astrophysics

6

Celestial Mechanics, Gravitational Effects, Many Body Problem, Planetary Orbits, Dynamic Characteristics, Equations Of Motion, Numerical Stability

Scientific paper

The paper treats the motion of n equal masses m located at each vertex of a regular polygon around a primary mass M. It is shown that when n is less than 7, this solution of equilibrium is unstable for any value of m. Also, if n is less than or equal to 7, the solution can be stable (linear stability) if m is sufficiently small; the maximum value of m is a function of n only. For each value greater than or equal to 7 and less than or equal to 100, the value of m is calculated which allows a stable solution. This is shown to make Maxwell's evaluation quantitatively precise.

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