On the existence of libration points in the spatial collinear restricted four-body problem within frame of repulsive Manev potential and variable mass

Abstract

The present paper deals with the spatial collinear restricted four-body problem within the frame of repulsive Manev potential (−1r+er2),e>0 and variable mass. We have revealed that how the parameters involved due to variable mass of the infinitesimal body influence the locations as well as number of libration points. Moreover, it is observed that the libration points exist only on the coordinate axes. The regions of possible motion are highly influenced by the Manev parameter, parameter occur due to variable mass of the infinitesimal body as well as by the Jacobian constant. Further, it is unveiled that the libration points are unstable for all the involved parameters.