Article

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

03/2006;
Source: arXiv

ABSTRACT In this paper we have studied non-linear stability of triangular equilibrium points. We have performed first order normalization in the generalized photogravitational restricted three body problem with Poynting-Robertson drag. In this problem we have taken bigger primary as source of radiation and smaller primary is an oblate spheroid. At first we have expanded the Lagrangian function in power series of x and y, where (x, y) are the coordinates of the triangular equilibrium points. Then the relation between the roots of the characteristic equation for the linearised system is obtained. Key Words:First order normalization / Generalised Photogravitational/ RTBP.

0 0
·
0 Bookmarks
·
20 Views
• Source
##### Article:Second Order Normalization in the Generalized Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag
[show abstract] [hide abstract]
ABSTRACT: In this paper we have performed second order normalization in the generalised photogravitaional restricted three body problem with Poynting-Robertson drag. We have performed Birkhoff's normalization of the Hamiltonian. For this we have utilised Henrard's method and expanded the coordinates of the third body in Double d'Alembert series. We have found the values of first and second order components. The second order components are obtained as solutions of the two partial differential equations. We have employed the first condition of KAM theorem in solving these equations. The first and second order components are affected by radiation pressure, oblateness and P-R drag. Finaly we obtained the third order part \$H_3\$ of the Hamiltonian in \$I_1^{1/2}I_2^{1/2}\$ zero.
03/2006;

Available from
17 Dec 2012

### Keywords

body problem

characteristic equation

first order normalization

Lagrangian function

linearised system

non-linear stability

oblate spheroid

power series