Symbolic Calculations in Studying the Problem of Three Bodies with Variable Masses

摘要

The classical problem of three bodies with variable masses is considered in the case when the masses of all three bodies vary isotropically. Solutions to the equation of motion in terms of the osculating elements of the aperiodic quasi-conical motion and the secular perturbations of the orbital elements of the system are examined. An algorithm for calculating the secular part of the perturbing functions and derivation of the differential equations determining the secular perturbations of the orbital elements are discussed. All the relevant symbolic calculations are carried out using the Mathematica computer algebra system.