Second Order Normalization in the Generalized Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag

摘要

In this paper we have performed second order normalization in the generalisedphotogravitaional restricted three body problem with Poynting-Robertson drag.We have performed Birkhoff's normalization of the Hamiltonian. For this we haveutilised Henrard's method and expanded the coordinates of the third body inDouble d'Alembert series. We have found the values of first and second ordercomponents. The second order components are obtained as solutions of the twopartial differential equations. We have employed the first condition of KAMtheorem in solving these equations. The first and second order components areaffected by radiation pressure, oblateness and P-R drag. Finaly we obtained thethird order part $H_3$ of the Hamiltonian in $I_1^{1/2}I_2^{1/2}$ zero.