The computation of characteristic exponents in the planar restricted problem of three bodies

Abstract

view Abstract Citations (34) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The computation of characteristic exponents in the planar restricted problem of three bodies Deprit, Andre ; Price, J. F. Abstract The canonical equations of motion in barycentric synodical Cartesian coordinates and momenta are integrable by means of recurrent power series; these series are proved to be convergent for initial conditions anywhere in the phase space except in the two phase planes of binary collisions. The integration by recurrent power series is extended to the variation equations. It is used to compute the monodromy matrix associated to the fundamental period of a periodic orbit. A simple formula is de- rived, which relates the trace of the monodromy matrix and the characteristic exponents. These numerical methods are applied to evaluate the characteristic exponents of Rabe's Trojan orbits; they are found to be of the stable type for the ovals, and of the unstable type for the horseshoe shaped orbit. When the periodic orbit is symmetric with respect to the axis of syzygies, four independent variational solutions computed only over half the period are shown to be sufficient for evaluating the characteristic exponents. Publication: The Astronomical Journal Pub Date: December 1965 DOI: 10.1086/109823 Bibcode: 1965AJ.....70..836D full text sources ADS |