Differential equations for the nonangular elements of a hyperbolic orbit

Differential equations are presented for the nonangular elements (semimajor axis, eccentricity, and inclination) of an intermediate hyperbolic orbit of a mass point moving in the gravitational field of a condensed planet, subject to a perturbation by another planet. The intermediate orbit is based on the symmetric variant of the problem of two fixed centers. The perturbation function is taken in the form of the Hill term in the expansion of the potential due to the perturbing planet, corrected for the elliptical character of its motion. The righthand sides of the equations are in the form of trigonometric series whose arguments are combinations of the angular elements of the intermediate motion of the mass point and the angular elements of the perturbing body, whereas the amplitudes depend on the nonangular elements of the two and are series In powers of the small parameter of the problem of two fixed centers.