Abstract

On averaging in systems with small Hamiltonianand much smaller non-Hamiltonian perturbations

Anatoly Neishtadt
Space Research Institute

A system which differs from an integrable Hamiltonian system with two degrees of freedom by a small Hamiltonian perturbation and much smaller non-Hamiltonian perturbation is considered. An example is motion of two satellites of a planet under the action of Newtonian attraction to the planet, of mutual Newtonian attraction (this is Hamiltonian perturbation) and of tidal friction (this is non-Hamiltonian perturbation). The unperturbed system is isoenergetically nondegenerate. The averaging method is used for approximate description of solutions of exact system on
time interval inversely proportional to amplitude of the
non-Hamiltonian perturbation. The averaged over initial
conditions error of this description is estimated from above by a value proportional to the square root of the amplitude of the Hamiltonian perturbation.