Evolution equations of the multi-planetary problem with variable masses

We investigated the influence of the variability of the masses of planets and the parent star on the dynamic evolution of n planetary systems, considering that the masses of bodies change isotropically with different rates. The methods of canonical perturbation theory, which developed on the basis of aperiodic motion over a quasi-conical cross section and methods of computer algebra were used. 4n evolutionary equations were obtained in analogues of Poincare elements. As an example, the evolutionary equations of the three-planet exosystem K2 − 3 were obtained explicitly, which is a system of 12 linear non-autonomous differential equations. Further, the evolutionary equations will be investigated numerically.