The characteristic exponents in the restricted problem of three bodies

Details The characteristic exponents in the restricted problem of three bodies The characteristic exponents in the restricted problem of three bodies

Oct 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980jmps...14..397i&link_type=abstract

Journal of Mathematical and Physical Sciences, vol. 14, Oct. 1980, p. 397-414.

Mathematics

Celestial Mechanics, Motion Stability, Three Body Problem, Floquet Theorem, Hamiltonian Functions, Matrices (Mathematics), Orbital Mechanics, Power Series, Variational Principles

Scientific paper

The restricted three-body problem is studied in a three-dimensional coordinate system. The Hamiltonian is defined for three bodies, as are the canonical equations of motion, and the solution is assumed in terms of powers of delta-t. The coefficients are evaluated by substitution in the system of differential equations and then by equating the coefficients. A dominating convergent series is found for each series and provides the range of convergence with an upper bound. The first order variations of the solution are examined, considering the power series solutions of the differential equations and their convergence. Finally, Floquet's theorem is used to obtain the characteristic exponents for the circular restricted problem of three bodies. A fourth degree equation is derived and the trace of the characteristic determinant is calculated to gain a general estimate of the stability of motion.

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