Explicit semianalytical theory of asteroid motion

A new semianalytical theory of asteroid motion is presented. The theory is developed on the basis of Kaula's expansion of the disturbing function incl uding terms up to the second order with respect to the masses of disturbing bodies. The theory is constructed in explicit form that gives the possibil ity to study separately the influence of different perturbations in the dyn amics of minor planets. The mean-motion resonances with major planets as we ll as mixed three-body resonances can also be taken into account. For the n on-resonant case the formulas obtained can be used for deriving the second transformation to calculate the proper elements of an asteroid orbit in clo sed form with respect to inclinations and eccentricities.