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

2006/02/23 by B. S. Kushvah, Badam Singh Kushvah, J.P. Sharma +5
Engineering · Mathematics · Physics and Astronomy · #70F15 #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies #math.DS #msc:70F15

paper · pdf · doi:10.48550/arxiv.math/0602528

12pages, LaTeX

openalex publication_date 2006/02/23 · arxiv created 2006/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 H₃ of the Hamiltonian in I₁^1/2I₂^1/2 zero.

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