NON-LINEAR STABILITY OF L\(_4\) IN THE R3BP WHEN THE SMALLER PRIMARY IS A HETEROGENEOUS TRIAXIAL RIGID BODY WITH N LAYERS

Abstract

In the present paper, the non-linear stability of the triangular libration point (L₄) in the restricted three-body problem (R3BP) when less massive primary is a heterogeneous triaxial rigid body has been studied with the assumption that the primary has N layers having different densities.  Following the procedure of Birkhoff’s normalization, we normalized the Hamiltonian up to second order and the co-ordinates (x, y) are expanded in double D’Alembert series.  The non-linear stability of the triangular libration point is discussed by applying Moser’s modified version of Arnold’s theorem (1961) as well as following the procedure as adopted by Bhatnagar and Hallan (1983).  It is observed that Moser’s theorem is applicable in the range of linear stability, except for three mass ratios depending upon heterogeneous triaxial rigid body.