The stability parameters of three-dimensional periodic three-body orbits

Details The stability parameters of three-dimensional periodic three-body orbits The stability parameters of three-dimensional periodic three-body orbits

Jul 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988ap%26ss.146...19p&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 146, no. 1, July 1988, p. 19-26.

Astronomy and Astrophysics

Astrophysics

3

Orbital Mechanics, Three Body Problem, Variational Principles, Angular Momentum, Equations Of Motion, Numerical Integration, Numerical Stability

Scientific paper

Formulas containing the elements of the variational matrix are obtained which determine the linear 'isoenergetic' stability parameters of three-dimensional periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The conditions for stability, criticality, and bifurcation are briefly examined, and the stability determination procedure is tested in the determination of some three-dimensional periodic orbits of low inclination bifurcating from vertical-critical coplanar orbits.

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