Author(s)

M. R. Hassan¹, Md. Aminul Hassan², Payal Singh³, Vinay Kumar⁴, R. R. Thapa⁵

¹Department of Mathematics, S. M. College, T. M. Bhagalpur University, Bhagalpur, India.
²GTE, Bangalore, India.
³Research Scholar, T. M. Bhagalpur University, Bhagalpur, India.
⁴Department of Mathematics, Zakir Hussain College, University of Delhi, New Delhi, India.
⁵Department of Mathematics, P. G. Campus, Tribhuvan University, Biratnagar, Nepal.

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.

Autonomous Four-Body Problem, Regularization, Periodicity, Poincare Surfaces of Section, Collision Orbit, Zero Velocity Curves

Hassan, M. , Hassan, M. , Singh, P. , Kumar, V. and Thapa, R. (2017) Periodic Orbits of the First Kind in the Autonomous Four-body Problem with the Case of Collision. International Journal of Astronomy and Astrophysics, 7, 91-111. doi: 10.4236/ijaa.2017.72008.