2012/12/10 by M. Alvarez-Ramírez, J. K. Formiga, Alvarez-Ramírez, M. +10 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #70F07 #Dynamical Systems (math.DS) #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear physics research studies #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies #astro-ph.EP #math-ph #math.DS #math.MP #msc:70F07
paper · pdf · doi:10.48550/arxiv.1212.2179
20 pages, 3 figures
arxiv created 2012/12/10 · openalex publication_date 2012/12/10 · arxiv updated 2012/12/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We study the fourth-order stability of the triangular libration points in the absence of resonance for the three-body problem when the infinitesimal mass is affected not only by gravitation but also by light pressure from both primaries. A comprehensive summary of previous results is given, with some inaccuracies being corrected. The Lie triangle method is used to obtain the fourth-order Birkhoff normal form of the Hamiltonian, and the corresponding complex transformation to pre-normal form is given explicitly. We obtain an explicit expression for the determinant required by the Arnold-Moser theorem, and show that it is a rational function of the parameters, whose numerator is a fifth-order polynomial in the mass parameter. Particular cases where this polynomial reduces to a quartic are described. Our results reduce correctly to the purely gravitational case in the appropriate limits, and extend numerical work by previous authors.