Effect of perturbed potentials on the non-linear stability of libration pointL 4 in the restricted problem

The non-linear stability of the libration pointL ₄ in the restricted problem has been studied when there are perturbations in the potentials between the bodies. It is seen that the pointL ₄ is stable for all mass ratios in the range of linear stability except for three mass ratios depending upon the perturbing functions. The theory is applied to the following four cases:

(i)	There are no perturbations in the potentials (classical problem).
(ii)	Only the bigger primary is an oblate spheroid whose axis of symmetry is perpendicular to the plane of relative motion (circular) of the primaries.
(iii)	Both the primaries are oblate spheroids whose axes of symmetry are perpendicular to the plane of relative motion (circular) of the primaries.
(iv)	The primaries are spherical in shape and the bigger is a source of radiation.