A simplification in the calculation of the characteristic exponents of the plane circular model of three bodies

It is shown that, to evaluate the two nontrivial characteristic exponents of the plane circular model of three bodies, we need only to integrate the variational equation fortwo displacements, rather thanfour, as is usually done. The two displacements should be chosen to lie in the constant Jacobi manifold and to be initially perpendicular to the given periodic motion. This simplification is applicable to both general orbits (integration over one whole period) and symmetric orbits (integration over one half period).