On new series in the problem of Routh's critical masses in the restricted planar three body problem

Details On new series in the problem of Routh's critical masses in the restricted planar three body problem On new series in the problem of Routh's critical masses in the restricted planar three body problem

Nov 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..12..327r&link_type=abstract

Celestial Mechanics, vol. 12, Nov. 1975, p. 327-336. In French.

Mathematics

4

Celestial Mechanics, Eigenvalues, Mass Ratios, Series (Mathematics), Three Body Problem, Critical Mass, Hamiltonian Functions, Lagrangian Equilibrium Points, Orbital Mechanics

Scientific paper

The planar restricted three body problem, linearized in the neighborhood of Lagrangian equilibria, has in general two eigenvalues and their opposites. The problem is here solved for the case of Routh's critical masses, where the eigenvalues are equal, by using normalized variables, which leads to expansions with fractional exponents. It is shown that normalized variables generate integer series in the non-resonant cases, series with negative exponents in the case of resonance where k is greater than or equal to zero, and series with fractional exponents when the resonance is equal to 1.

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