Periodic Orbits of the First Kind in the Autonomous Four-body Problem with the Case of Collision

M. R. Hassan, Md. Aminul Hassan, Payal Singh, Vinay Kumar, R. R. Thapa
2017 International Journal of Astronomy and Astrophysics International Journal of Astronomy and Astrophysics  
In this manuscript, the existence of periodic orbits of collision of the first kind has been discussed on the model of Autonomous Four-body Problem by the method of analytic continuation given by Giacaglia [1] and Bhatnagar [2] [3] . For the existence of periodic orbits, Duboshin's criterion [4] has been satisfied and it has been confirmed by analyzing the Poincare surfaces of section (PSS) [5] . Also it has been shown that the case of collision given by [7] is conserved by the method analytic
more » ... he method analytic continuation. In all sections of this manuscript, equilateral triangular configuration given by Ceccaroni and Biggs [8] has been considered. In this model, third primary of inferior mass (in comparison of the other primaries) is placed at the equilibrium point 4 L of the R3BP.
doi:10.4236/ijaa.2017.72008 fatcat:6uzqez2vsrdinntaa7zglxrkae