TITLE:
Periodic Orbits of the First Kind in the Autonomous Four-body Problem with the Case of Collision
AUTHORS:
M. R. Hassan, Md. Aminul Hassan, Payal Singh, Vinay Kumar, R. R. Thapa
KEYWORDS:
Autonomous Four-Body Problem, Regularization, Periodicity, Poincare Surfaces of Section, Collision Orbit, Zero Velocity Curves
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.7 No.2,
June
12,
2017
ABSTRACT: 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 Levi-Civita [6] [7] is conserved by the 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 L4 inferior mass (in comparison of the other primaries) is placed at the equilibrium point of the R3BP.