About averaging procedures in the problem of asteroid motion

Abstract

A new mathematically correct approach to construct an averaging procedure for the motion of a massless body around the central body perturbed by fully interacting planets is developed and the errors of the standard solution are discussed. The new technique allows to combine the advantages of the Hamiltonian representation with the usage of standard osculating elements in combination with all the standard expansions of the perturbing functions. The main idea is to introduce new additional variables conjugate to all the standard elements and to work in a corresponding super phase space. In this way, the number of variables is doubled at first, but one has to deal with only one Hamiltonian. The artificially introduced variables disappear from the final averaged equations as well as from the transformation formulae connecting the osculating and the mean elements.

A First Order Automated Lie Transform

“…Tupikova [32] gives a mathematical approach for constructing an averaging procedure for the motion of a massless body around the central body perturbed by fully interacting planets. Carvalho et el.…”